Algebra

Problem 119

Sir Sagar0

Problem 119

In a family with two children, what are the probabilities of the following outcomes, assuming that the birth of boys and girls is equally likely?

 

Solution

 

Boys and girls is equally likely so in two children al have probability \frac{1}{2}

p(boy) = \frac{1}{2}

p(girl) = \frac{1}{2}

 

a. Both are boys.

When both are boys then probability (BB) = \frac{1}{2} \ast \frac{1}{2} = \frac{1}{4}

 

b. The first is a girl and the second a boy.

When first is a girl and second is a boy then propability (GB) = \frac{1}{2} \ast \frac{1}{2} = \frac{1}{4}

 

c. Neither is a girl

Neither girl is girl means al are boys same case like part a

P(neither is a girl ) = \frac{1}{2} \ast \frac{1}{2} = frac{1}{4}

 

d. At least one is a girl

Total case of at least one girl = (GG), (G, B) , (B, G)

So probability = GG + GB + BG =  \frac{1}{2} \ast \frac{1}{2} + \frac{1}{2} \ast \frac{1}{2} + \frac{1}{2} \ast \frac{1}{2} = \frac{1}{4} +\frac{1}{4} +\frac{1}{4} = \frac{3}{4}

 

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