Question

Out of 750 families with 4 children each, how many families would be expected to have atleast one boy 

Answer 1

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) = nc_xp^xq^n-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)