Question 1001764: A bird breeder has a total of 50 canaries 21 of which are male and 29 of which are female. A pet shop randomly selects 8 of them. Find the following probabilities. Remember to decide first if the order matters when making the solution round to six decimal places.
Question 1) What is the probability that at least six of the eight are female. Hint at least six means either 6, or 7, or 8.
Question 2) What is the Probability that at least two of the eight are males.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! can do this by 8 choose 6 with the given probabilities of 58% and 42%
also can do it by knowing order doesn't matter, and one form of the 28 ways can choose 6 from 8 8!/6!2!
the six might be the first six
29/50 *28/49*27/48*26/47*25/46*24/44*21/43*20/42.
The denominator stays the same for all 28 ways. The numerator is the same, too, but it is multiplied in a different order.
28(0.58^6)(0.42)^2=0.188029
8(0.58^7)(0.42)=0.074188 because there are only 8 ways to choose 7.
(0.58^8)=0.012806
The total is 0.275023
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at least 2 are males
do 0,1, and subtract from 1
p(0)=p(8 females)=0.012806
p(1)=p(7 females)=0.074188
They add to 0.086994
subtract from 1, because we don't want these, and get 0.913006.
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