Question

X 4.5.13 In a certain country, the true probability of a baby being a boy is 0.537. Among the next four randomly selected births in the country, what is the probability that at leas The probability is (Round to three decimal places as needed.)

Answer 1

$\small \mathbf{Solution}$

given : n 4, P(girl) = 0.537, p(boy) 1-p(girl) 1-0.5370.463

q(not boy) p(girl) = 0.537

formula P(X = r) C p * q' n-T where, TC r!(n-r

Pat least one of them is boy) P(X > 1]

P(X1) 1- P(X< 1)

P(X1) 1- P(X = 0)

P(X 1) 1- {C 0.4630 0.537 10

4! P(X 1) 1 O! (4-0*0.4630 0.5374-0

4! 0.4630 0.5374-0 P(X 1) 1 O!4!

P(X 2 1) 1 {1 1 0.537 1

$\small P(X\geq 1)=1-\left \{ 0.083 \right \}$

P(X10.917

. The probability is 0.917