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Question
Out of 750 families with 4 children each, how many families would be expected to have atleast one boy
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Solution
Assume equal probabilities for boys and girls
Let p be the probability of having a boy
Let x be the random variable for getting either a boy or a girl
∴ p = `1/2` and q = `1/2` and n = 4
In binomial distribution P(X = 4) = ncxpxqn-x
Here the binomial distribution is P(X= x) = `4"C"_x (1/2)^x (1/2)^("n" - x)`
P(atleast one boy) = P(X ≥ 1)
= 1 – P(X < 1)
= `1 - 4"C"_0 (1/2)^0 (1/2)^(4 - 0)`
= `1 - (1)(1)(1/2)^4`
= `1 - 1/16`
= 1 – 0.0625
= 0.9375
For 750 families (P ≥ 1) = 750 × 0.9375
= 703.125
= 703 ........(approximately)
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