We assume the a child is either a boy or a girl. Therefore
the probability that a child is a boy = 1/2. Also the probability that child is a girl
= 1/2
Therefore the event of at least one boy out 3
children includes the event of one boy and 2 girls, 2 boys and 1 girl, all 3 boys
.
The probability that one child is a boy and 2 are girls =
3C1*(1/2) {1-1/2}^2 = 3/8.
The probability that 2 are boys
and one is girl = 3C2*(1/2)^2 {1-1/2} =3/8
The pobability
that all 3 are boys = 3C3*(1/2)^3 = 1/8
Therefore the
required probability of at leat least one child is boy out of 3 children = 3/8+3/8+1/8
= 7/8.
Alternatively , probability of at least one out of 3
chidren is a boy is equivalent to the probability of not all 3 are girls. Probability
that all three children are girls = (1/2)^3 = 1/8. Therefore the probability that not
all three children are girls is 1-1/8 = 7/8.
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