SOLUTION: An endurance contest is being held with two independent groups of 12 participants. Individual participants in the contest drop out before the end of the contest with probability 0.

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Question 995519: An endurance contest is being held with two independent groups of 12 participants. Individual participants in the contest drop out before the end of the contest with probability 0.18 (independently of other participants). What is the probability that at least 11 participants complete the endurance contest in one of the two groups, but not in both groups?
Answer by Theo(13342) About Me  (Show Source):
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the probability of not passing the test is .18.
the probability of passing the test is 1 - .18 = .82.

the probability of all 12 passing the test in one group is .82^12 = .0924200563
the probability of 11 passing the test and 1 failing the test in one group is .82^11 * .18^1 * 12 = .2434479531.

the probability of 11 or more passing the test in one group is .0924... + .2434... = .3358680094

the probability of 11 or more not passing the test in one group is 1 - .3358... = .6641319906

you have two groups.

the probability that only one of the groups will have 11 or more participants complete the test is equal to:

.3358... * .6641... * 2 = .4461213793

the probability that both groups have 11 or more participants complete the test is equal to:

.3358... * .3358... = .1128073197

the probability that both groups will not have 11 or more participants complete the test is equal to:

.6641... * .6641... = .441071301

total probability is .4461213793 + .1128073197 + .441071301 = 1 as it should be.