Probability(1B,2G) = Favorable choices of having exactly 1B and 2G/Total number of Possiblities of sexes for 3 children

Let's do the sample set:

Represent Girls with G and Boys with B

3 children can have following possibilities of sexes

GGG - 3 girls

GGB - 2 girls one boy

GBG

GBB

BGG

BGB

BBG

BBB

Total possibilities of both sexes = 8

Number of choices where there are exactly 2 girls and 1 boy are:

GGB

GBG

BGG

=3.

Thus, probability = 3/8

Ans: "D"

This problem is similar to having exactly 2 heads in 3 tosses.

Alternate way;

The total number of possibilities = (Number of possible outcomes in each flip)^(Number of tosses) = 2^3=8

Likewise;

The total number possible sexes for 3 children = (Number of possible sex for each child)^(Number of children)

Number of possible sex for each child = 2 = (Boy or Girl)

Number of children = 3

Total possible sexes = 2^3 = 8

Possibilities to have exactly 2 Girls out of 3 child and 1 Boy out of remaining 1 Child:

=

\(C^{3}_{2}*C^{1}{1} = 3\)

Thus, probability = Favorable/total outcomes = 3/8.

_________________

~fluke

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