A family has two children. If B represents a boy and G represents a girl, the set of outcomes for the possible genders of the children is S = {BB, BG, GB, GG}, with the oldest child listed first in each pair. Let X represent the number of times G occurs. Which of the following is the probability distribution, PX (x) ?

Question

Mathematics

Lyric Pearson

22 February, 10:59

A family has two children. If B represents a boy and G represents a girl, the set of outcomes for the possible genders of the children is S = {BB, BG, GB, GG}, with the oldest child listed first in each pair. Let X represent the number of times G occurs. Which of the following is the probability distribution, PX (x) ?

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Answers (1)

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Mariyah Hoffman · Answer 1

Determine how many times G occurred in the set of outcomes given.

So,

BB = G never occurred = 0

BG = G occurred once out of 2 = 1/2

GB = G occurred once out of 2 = 1/2

GG = G occurred twice = 2/2 or 1

So, the probability distribution is 0, 1/2, 1/2, and 1.