一條數學 急用15分

It is given in the question that
P(boy) = 0.45

Assume that the gender of each child is independent of others.

(a)
P(2 boys)
= P(boy and boy)
= P(boy) × P(boy)
= 0.45 × 0.45
= 0.2025

(b)
P(at least 1 boy)
= 1 - P(no boy)
= 1 - P(not boy and not boy)
= 1 - P(not boy) × P(not boy)
= 1 - (1 - 0.45) × (1 - 0.45)
= 1 - (1 - 0.45)²
= 1 - 0.55²
= 1 - 0.3025
= 0.6975


2015-04-12 15:36:20 補充：
(b) Alternative method:

Possibilties are
(1) Boy, Girl
(2) Girl, Boy
(3) Boy, Boy

Probability
= 0.45 × 0.55 + 0.55 × 0.45 + 0.45 × 0.45
= 2(0.45)(0.55) + 0.45²
= 0.495 + 0.2025
= 0.6975

2015-04-12 18:23:29 補充：
若 (a) 題目修正為
A family prepares to have 3 children. find the probabilities that all of them are
boys.

那麼答案就是：
(0.45)³ = 0.091125

2015-04-12 18:23:39 補充：
若 (a) 題目修正為
A family prepares to have 3 children. find the probabilities that all of them are
boys.

那麼答案就是：
(0.45)³ = 0.091125

(a)個條係3 children打少左一個