A couple is planning to have 3 children. Assuming that having a boy and having a

Question

A couple is planning to have 3 children. Assuming that having a boy and having a girl are equally likely, and that the gender of one child has no influence on (or, is independent of) the gender of another.

a What is the sample space in this case? (Use B for boy and G for girl).

b Since both genders are equally likely, and since the gender of one child does not affect the gender of another, in this scenario all 8 outcomes are equally likely (each having probability 1/8). Now we're getting to our event of interest: "Having exactly two girls." Let's denote this event by A. How many of the 8 outcomes satisfy (or make up) event A? List them.

c We now have all we need in order to find P(A). What is P(A), the probability of a family with three children having exactly two girls?

Explanation / Answer

(a)

S = {BBB, BBG, BGB, GBB, BGG, GBG, GGB, GGG}

(b)

A = {BGG, GBG, GGB}

(c)

P(A) = (1/8)3 = 0.0020

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