Question

For the Vulcan species, if the probability that a couple produces a girl is 0.97216, and if the couple has 7 children, what is the probability they will have: 5 boy(s) and 2 girl(s) (in any order)?

Please show work! I used (7C2)(.97216^2)(.022784^5) and got .000000332 but i'm not sure if that is correct.

Answer 1

Probability of producing a girl = 0.97216

By law of total probability,

probability of producing a boy = 1- 0.97216 = 0.02784

Required probability : out of 7 children, 5 boys and 2 girls.

Since order does not matter, we will use combination.

2 out of 7 children are girls, so we first select 2 children out of the 7 children = 7C2

Now, probability that the selected children are girls = 0.97216²

The remaining 5 children must be boys.

The probability of those 5 children are boys = 0.022784^5

So, the required probability will be : (7C2) (0.97216²)(0.022784^5)

= 0.000000332

answered by: anonymous