suppose noah started with 36 pairs of animals on the ark and

suppose noah started with 36 pairs of animals on the ark and 8 of them died. If fate chose the 8 at random, what is the expect number of complete pairs left

Solution

No of pairs = 36

No of animals =72

Number died =8

These 8 can be either all males or females or both

i.e. if no of males died =x and no of females died = y, then x+y =8

x can take values as 0 to 8 and y 0 to 8-x

f(x) =K 36Cx(36C8-x), x =0,1,2...8 and K is suitable constant for making pdf = 1

This is a discrete distribution

There are two outcomes either male or female

p = Prob for male dying = 0.5 and q =0.5

Hence Expected value of x = np = 4

Expected no of complete pairs left = 36-4 = 32