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Question
In a family of 3 children, what is the probability that there will be exactly 2 girls?
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Solution
Let p be the probability of getting a girl child
= `1/2` q
= 1 – p
⇒ = `1 – 1/2`
∴ q = `1/2` and n = 3
In a binomial distibution
P(X = x) ncx pxqn-x
P(exactly 2 girls) P(X = 2)
= `3""_2 (1/2)^2 (1/2)^(3 - 2)`
= `(3 xx 2)/(1 xx 2) (1/4) xx (1/2)`
= `3 xx(1/8)`
= `3/8`
= 0.375
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