Answer:
Susan should pick 6 cherries from box, so the probability of picking the 2 rotten cherries is 1/20
Step-by-step explanation:
assuming that each cherry is equally probable to be chosen , since each cherry is independent from the others and sampling is done without replacement , the random variable X= number of cherries that are rotten from the picked ones follows a hyper geometrical distribution , where
P(X=k)= C(M,k) * C(N-M, n-k) / C(N,n)
where
N= population size = 25
n= number of picks
M = total number of rotten cherries =2
k = number of rotten cherries picked =2
C( ) = combination
then
1/20=C(2,2)*C(25-2,n-2)/C(25,n) = 1 * (23!/(n-2)!*(25-n)! / (25!/(n!*(25-n)!
1/20 = n!/(n-2)! * 1/(24*25)
24*25/20 = n*(n-1)
n²-n-30 =0
n= (1 +√(1+4*1*30))/2 = 12/2= 6
n=6
then Susan should pick 6 cherries from box, so the probability of picking the 2 rotten cherries is 1/20
