The probability of a woman's pregnancy

Question

The probability of a woman's pregnancy will exceed 9 month is 0.314. In 6 human births, what is the probability that the number of births will exceed 9 months is:
1. Exactly 3
2. Exactly 5
3. At least 5

Answer 1

1) 6C3 * (.314)^3 * (1-.314)^(6-3)

 =.2

 

2)  6C5 * (.314)^5 * (1-.314)^(6-5)

=.0125

 

3) P(at least 5) = P(0-5) = 1 - P(6)

 

= 1 - [6C6 * (.314)^6 * (1-.314)^(6-6)]

= 1 - .0009

= .9991