If a couple were planning to have three children, the sample space summarizing t

Question

If a couple were planning to have three children, the sample space summarizing the gender outcomes would be: bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg. a. Construct a similar sample space for the possible gender outcomes (using b for boy and g for girl) of two children. b. Assuming that the outcomes listed in part (a) were equally likely, find the probability of getting two girl children. c. Find the probability of getting exactly one boy child and one girl child. a. What is the sample space? b. Find the probability of getting two girl children c. Find the probability of getting one boy child and one girl child.

Explanation / Answer

(a)

Following is the required sample space:

S = {bb, bg, gb, gg}

(b)

Out of four possible outcome, 1 outcome (gg) has two girls. So the probabaility of getting 2 girls is

P(two girls) = 1/4 = 0.25

(c)

Out of four possible outcome, 2 outocmes (bg, gb) has one boy and one girl. So the probabaility of getting one boy and one girl is

P(one boy and one girl) = 2/4 = 0.5

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