2. A couple plans to have three children The probability of any given child bein

Question

2. A couple plans to have three children The probability of any given child being female is 0.5. The gender of each child is an independent event (the gender of the second child does not depend on or have anything to do with the gender of the first child; the gender of the third child does not depend on the gender of the first child or the second child) Write out all outcomes in the sample space fo eh genders of the three children a. b. What should be the probability associated with getting two girls and one boy? SHOW YOUR WORK

Explanation / Answer

B- Boy ; Probability of having a boy = P(B) = 0.5

G-Girl : Probability of having a girl = P(G) = 0.5

Three children

The sample space for three chilrdren -

BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG

Sample space for getting two girls and a boy:

BGG, GBG, GGB

Probability of getting two girls and one boy = P(BGG or GBG or GGB) (The events BGG, GBG and GGB are mutually exclusive)

By addition theorem,

P(BGG or GBG or GGB) = P(BGG) + P(GBG) + P(GGB)

By multiplication theorem, P(BGG)=P(B)P(G)P(G) = 0.5x0.5x0.5 = 0.125

P(GBG) = P(G)P(B)P(G) = 0.5x0.5x0.5 = 0.125

P(GGB) = P(G)P(G)P(B) = 0.5x0.5x0.5 = 0.125

P(BGG or GBG or GGB) = P(BGG) + P(GBG) + P(GGB) = 0.125+0.125+0.125=0.375

Probability of getting two girls and one boy =0.375

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