BOWMAN, Circuit Judge.

Appellant Vernon Johnson was convicted after a jury trial of attempting to possess with intent to distribute more than five hundred grams of cocaine. 21 U.S.C. § 841(a)(1), 846 (1988). Johnson appeals his conviction, arguing that the District Court should have excluded evidence taken from his home because agents of the Drug Enforcement Agency had seized the evidence after entering his home without a search warrant. The government argues that obtaining a warrant was infeasible and that the agents were compelled to enter without a warrant because of exigent circumstances. We affirm.

The investigation that led to Johnson's arrest began when a package sent in the overnight express mail from Los Angeles to St. Louis aroused the suspicions of a postal inspector in Los Angeles. After advising Inspector Hearne, the postal inspector in St. Louis, of his hunch that the package contained narcotics, the inspector in Los Angeles forwarded the package to St. Louis at Inspector Hearne's request. When the package arrived in St. Louis, Inspector Hearne arranged for a trained dog to sniff the package. On the basis of the dog's reaction, which indicated the presence of controlled narcotics, the inspector applied for and received a search warrant to open the package. Within the package he found a one kilo block of pure cocaine and two bottles containing one half of a kilo of procaine, a substance commonly used to dilute cocaine prior to distribution. The inspector then applied for and received a warrant to place a transmitting device inside the package in order to effect a controlled delivery. The original contents of the package were removed and the device was enclosed, along with a stack of index cards, a can of soda, and a bottle of Maalox meant to simulate the brick of cocaine and the bottles of procaine. Transcript Vol. I at 34-35.

At this point the postal inspector was joined by several agents from the Drug Enforcement Agency. Their plan to make a controlled delivery of the package was complicated by the fact that the package was improperly addressed. Johnson's counsel at trial described the opacity of the mailing label in her opening argument:

When the Express Mail package arrived in St. Louis it was addressed to a non-existant [sic] address or location. The address could not be located in a criss-cross directory. The Postal Service had to surmise what address this package should be delivered to. There are misspellings. The street is misspelled. The city is listed as Normandy and the state is listed as Lucas and Hunt. There are three very important errors just on the label.

Transcript Vol. I at 22. The address the agents settled on as that most similar to the one on the mailing label turned out to be Vernon Johnson's address. (The package was addressed to "Albert Nixson.") Over the course of the next three days the agents attempted four times to deliver the package to Johnson's address before the door was answered. The man who finally answered the door stated that Albert Nixson would be back soon and accepted the package, signing the name "J. Peters." About ten minutes after the package was delivered, the appellant was seen entering the apartment. A few minutes after that, two men, including the man who had signed for the package, departed.

Shortly thereafter, the agents monitoring the transmitter lost the signal completely. The transmitter was not a tracking device but, rather, had the capacity to indicate when the package was being opened by sending a more rapid signal. Because the transmissions from the device simply stopped altogether without indicating that the package had been opened, the agents became concerned that the device had been found and dismantled. If the occupants had found the transmitter, the agents feared that they would destroy other evidence. The agents, therefore, decided to enter the apartment. When in response to their loud knocks on the door and shouts of "Police! Open the door!" they heard only the sound of footsteps rapidly retreating from the door, they broke down the door with a battering ram and entered the apartment.

As the agents entered the apartment, Johnson emerged from the bathroom with his hands in the air. In the bathroom the agents found the index cards that had been planted in the package to simulate the cocaine brick in the original contents. The cards had been dumped in the commode and the brown paper wrapping discarded on the floor by its side. Immediately after entry, some of the agents had scanned the apartment for additional suspects. Although they found no one else in the apartment, during the course of this survey they did find and seize various drug paraphernalia that were in plain view.

Johnson argues that the evidence seized during this entry should have been excluded at trial because the agents entered without a warrant. He does not contest that the evidence taken was in the agents' plain view. Rather, he contends that the government's claim to exigent circumstances is inapposite because the agents could have obtained a warrant for a search of Johnson's home prior to their execution of the controlled delivery.

If the address on the package had identified a real person at an accurate address, Johnson would have at least a colorable claim. If, in addition, this package had not been the first shred of evidence suggesting the existence of a narcotics operation, but rather had arrived in the mail during the denouement of a governmental investigation of Johnson, he would have a compelling argument. Indeed, it would have been a serious omission for the agents not to have applied for a search warrant had they known in advance that Vernon Johnson was the intended recipient of the package; that he, or someone at that address, would be willing to accept delivery of the package; and that Johnson's apartment was in fact the situs of a drug operation. It also, we might add, would have been an omission completely incongruous with the agents' meticulous behavior in the investigation of this drug shipment up until that point. As is generally the case with stories that depend upon the concerted irrational behavior of multiple individuals, Johnson's description of events in this case does not conform to the facts.

The agents knew neither whether the address they credited the package label with describing was the intended address, nor whether the occupant of that address would be willing to accept the package. Secreting a transmitter within the package would have been rather redundant had there been no reason to doubt that the agents were delivering the package to its final destination. Moreover, there would have been no reason for the agents not to have applied for, and a magistrate not to grant, a search warrant. There was, however, a great deal of doubt surrounding the controlled delivery in this case because the agents were not at all sure where the final resting place of the package was to be. Using hindsight as his handmaiden, Johnson attempts to obscure this uncertainty, but our task is to "judge the constitutionality of [the agents'] conduct in light of the information available to them at the time they acted," and not on the basis of what is known retrospectively. Maryland v. Garrison, 480 U.S. 79, 85, 107 S.Ct. 1013, 1017, 94 L.Ed.2d 72 (1987); see also United States v. Gallo-Roman, 816 F.2d 76, 80 (2d Cir. 1987).

Johnson's suggestion that the agents had sufficient information for a warrant prior to the time the package was finally accepted at his address must fall before the Fourth Amendment's mandate that "no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched." U.S. Const. amend. IV. Had the agents obtained a general warrant based on the information they had prior to the controlled delivery and then filled in the remaining details at the time of execution, this Court would have been compelled to condemn their conduct as violative of the Warrant Clause. See Lo-Ji Sales v. New York, 442 U.S. 319, 325, 99 S.Ct. 2319, 2323, 60 L.Ed.2d 920 (1979). Nor, it seems, could the agents simply have described the address they assumed had been intended, because "the information put forth [in a warrant affidavit must be] believed or appropriately accepted by the affiant as true," Franks v. Delaware, 438 U.S. 154, 165, 98 S.Ct. 2674, 2681, 57 L.Ed.2d 667 (1978), and the agents obviously had nontrivial doubts as to the intended mailing address of the package. In light of the false name given for the addressee and the numerous mistakes in the address itself these doubts were well-founded. The agents' assignation of Johnson's address to the package label is more properly described as their best guess than as an actual belief. Similarly, it is far from assured that a court would be willing to characterize this hunch as "appropriately accepted . . . as true."

Perhaps more importantly, though, Johnson's address might have been only a receiving depot for a larger operation somewhere else. In a case remarkably similar to this one — and in which we recognized the existence of exigent circumstances — this Court stated that officers conducting an investigation "were not required to seek a warrant as soon as they had probable cause to suspect a conspiracy to distribute cocaine [but] could legitimately wait in order to gather additional evidence." United States v. Palumbo, 735 F.2d 1095, 1097 (8th Cir.), cert. denied, 469 U.S. 934, 105 S.Ct. 332, 83 L.Ed.2d 268 (1984). In that case, we cited with approval the distinction drawn by the Fifth Circuit between a planned arrest and an impromptu arrest made during the investigative process itself. The Fifth Circuit had written:

The government is not compelled to effect an arrest upon the occurrence of probable cause to believe a crime has been committed. Rather, the government may await that move in the hope of ferreting out any hitherto unknown individuals involved in the illicit undertakings, gathering additional evidence substantiating the crimes believed to have been committed, or discovering any other offenses in which the suspects are involved. . . . [U]nlike the case of the "routine" felony arrest, where a given individual and a distinct crime is [sic] involved, the fluidity of an ongoing investigation of the distribution of narcotics makes the obtaining of an adequate search warrant more difficult to time in the flow of events. While the possibility of discovering additional participants or evidence of crimes does not negate the warrant requirement, we find that it is one factor to weigh in determining the reasonableness of the government's warrantless arrest.

United States v. Hultgren, 713 F.2d 79, 87 (5th Cir. 1983) (emphasis added).

Deference to the agents' modus operandi in this case is appropriate. A package of drugs with an indeterminate address label suddenly fell into the agents' hands. Moreover, as Johnson's counsel at trial noted, Johnson did not fit the pattern of "a person who's known to be involved in narcotics, someone who's distributing, something of this nature." Transcript Vol. I at 23. With no additional information about the package available to the agents, they had reason to question not only whether Johnson's address was the address intended on the package label, but also whether that address was the actual site of the criminal activity. Thus, the agents planted a transmitter within the package and kept the house and its occupants under close surveillance in order to discover the package's final destination. Because the delivery to Johnson's apartment might very well have turned out to be only the first step in the agents' investigation, they were not required to seek a warrant but "could legitimately wait in order to gather additional evidence." Palumbo, 735 F.2d at 1097.

It is irrelevant that there was a distinct possibility that, shortly after the package was delivered to Johnson's address, it would be opened and that the exigent circumstances created by the likelihood of evidence being destroyed were therefore foreseeable. In United States v. Palumbo, we explicitly stated that, because the exigency had not been manufactured by the officers, no amount of foreseeability could vitiate the officers' justification of exigent circumstances. 735 F.2d at 1097. Here, none of the factors converging to create exigent circumstances was within the agents' control.

As we already have observed, obtaining a valid search warrant would very likely have been impossible, as a result of a phony name and obscure address on the address label. Indeed, it is for the very purpose of evading detection that such fictional names and disarranged addresses are frequently employed by those who deal in drugs. If Johnson and his associates fear warrantless entries into their homes, they would be well advised to address their drug shipments to real people at clearly identifiable addresses. In that event, we would be somewhat less disposed to accept the government's claim of exigent circumstances in cases such as this. The practical impossibility of obtaining a valid warrant to search Johnson's home in this case, however, "resulted solely from the method by which [Johnson] chose to smuggle illicit drugs." United States v. Montoya de Hernandez, 473 U.S. 531, 544, 105 S.Ct. 3304, 3312, 87 L.Ed.2d 381 (1985). Similarly, that the discovery of this package was the first incident alerting the agents to criminal activity at Johnson's address was obviously not a purposeful manipulation of events by the agents toward the end of claiming exigent circumstances.

In retrospect, it is not entirely clear whether the immediate catalyst for the exigency itself — the failure of the transmitter to emit a signal — was caused by a malfunction of the transmitter or by its movement to an area within the apartment where the walls interfered with the signal's escape. But, in any event, it was not caused by the agents. Nor would the existence of exigent circumstances be diminished if upon the opening of the package the transmitter had performed properly and emitted a more rapid and high toned signal, as the postal inspector believed it did. That too would have been out of the agents' control and would have given rise to the concern that evidence was about to be destroyed.

Judge Arnold's dissent, post at 449, takes the view there is "nothing about this chain of events to distinguish it from what might well have happened if the package had been delivered to the home of a law-abiding citizen." We disagree. Although the package label was indefinite enough to prevent the issuance of a warrant — undoubtedly this is one of the purposes of the cryptic addresses employed by those who send illegal goods through the mail — it was not so indefinite as to permit the assertion that Johnson's address was, as likely as not, the apartment of a law-abiding citizen. Those who use the mails to traffic in illegal goods do not, after all, want their packages lost in the mail. The agents, of course, had no basis at all on which to conclude that Apartment E in the Lucas and Hunt apartment complex was the site of the main operation, but they could at least presume that it was fairly likely to be the intended first stop for the drugs.

In any event, the agents' claim to exigent circumstances does not rely solely on their having accurately deciphered the address label: much more occurred before they entered Johnson's apartment. First, the package was accepted at that address; second, the occupant of the apartment opened the package; and, third, the occupant did not respond to the announcement that the police were at his door but, rather, was heard dashing about inside the apartment. Judge Arnold's consideration of the first two events in isolation allows him to formulate the proposition that because there is a reasonable possibility that each one of these acts could independently happen to, or be done by, a law-abiding citizen such as himself, there is also a reasonable possibility that both of them could take place with reference to a law-abiding citizen. (Judge Arnold does not suggest that he, like Johnson, might run away from his door, should the police ever come to it.)

It is basic to the law of probabilities, however, that "[i]f events A and B are independent, the probability of the intersection of A and B equals the product of the probabilities of A and B." J. McClave P. Benson, Statistics for Business and Economics, 135 (1982). Assigning numerical estimates to the probabilities of these four events independently occurring in relation to a law-abiding citizen — estimates that we believe generously express Judge Arnold's concerns — demonstrates the extreme remoteness of any possibility that the factors comprising the exigency in this case could lead to a violation of the sanctity of the home of a law-abiding citizen. Suppose we assume that there is a 25% chance that the address at the Lucas and Hunt apartment complex on Englewood in the suburb of Normandy was not the intended address of the package containing cocaine, but rather the address of a law-abiding citizen; that there is a 25% chance that the occasional roommate of a law-abiding citizen would accept a package addressed not to the law-abiding citizen but to a person the roommate had never heard of; that there is a 25% chance that the law-abiding citizen would see that the package was addressed to someone he did not know, yet instead of returning it to the post office would open it; and finally that 25% would describe the odds that the law-abiding citizen would run away from the door when the police announced themselves. Even with these fairly liberal odds, one is left with a probability of 0.84% that the agents were at the door of a law-abiding citizen, and a probability of 99.16% that they were not. If we increase to 50% the probability of these four events occurring independently to a law-abiding citizen — an absurd exaggeration — we are still left with a probability of only 6.25% that the agents were at the door of a law-abiding citizen, and a probability of 93.75% that they were not. We think such extremely high odds that the occupant of that apartment was not a law-abiding citizen fully justifies an entry based on exigent circumstances.

For the reasons discussed above, the District Court did not err in admitting the evidence seized at Johnson's home. The judgment of the District Court is affirmed.