Question 995519
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.