Under certain conditions, there is a 0.015 probability that a randomly selected driver will fail a breathalyzer test. If the police test 10 random drivers, what is the probability of finding at least one driver who fails the test?
I know that it would have to be 1 minus the probability that no one fails the test but since they do the test 10 times, when I subtract .015 from 1, i get .985 (the probability they don't fail) so then I put that to the 10th power, but at that point it is larger than 1? am i doing this wrong?

Question

Under certain conditions, there is a 0.015 probability that a randomly selected driver will fail a breathalyzer test. If the police test 10 random drivers, what is the probability of finding at least one driver who fails the test?
I know that it would have to be 1 minus the probability that no one fails the test but since they do the test 10 times, when I subtract .015 from 1, i get .985 (the probability they don't fail) so then I put that to the 10th power, but at that point it is larger than 1? am i doing this wrong?

tkhunny · Answer

p(1 failure on 1 test) = 0.015
p(1 success on 1 test) = 1 - 0.015 = 0.985
p(10 success on 10 test) = (0.985)^10 < 1

You're not multiplying by 10.  You're multiplying by 0.985 < 1.

dunnitagainn · Answer

For some reason, before when I put (.985)^10 into my calculator i got something larger than one, but this time it worked, thank you!

dunnitagainn · Answer

@tkhunny I actually have another question if you could possibly help me?

dunnitagainn · Answer

if a jury list contains 20 men and 20 women, find the probability of selecting 12 members that are all men?
Would this be similar: 1-p(no men) ?

tkhunny · Answer

No good.  Post on another thread.  This is a finite population.