Suppose couples decide to have children until they either have a child of each s

Question

Suppose couples decide to have children until they either have a child of each sex or they have three children.Let the random variable X be the number of girls resulting from this approach. Assuming that births are independent and equally likely to be boys or girls, an incomplete probability function for X is as follows: 0 3 P(Xx) 0.625 0.125 Calculate the missing values in this table. Based on these probabilities, what is the expected number of girls, E(X), for a couple following this approach? a) 0.75 b) 1.00 c) 1.25 d) 1.50 e) 1.75

Explanation / Answer

(a)

For X = 0:

Number of girls = 0

So,

Number of boys = 3

P(X = 0) = P(3 boys) = 0.53 = 0.125

For X = 3

P(X = 3) = P(3 girls) = 0.53 = 0.125

Thus, Probability Function of X is given by:

x                         0                1             2               3

P(X=x)                 0.125         0.625    0.125         0.125

(b)

E(x) = (0X0.125) + (1X0.625)+(2X0.125)+(3X0.125)

       = 0.625 + 0.25 + 0.375

     = 1.25

So,

Correct option:

c) 1.25

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