# Binomial distribution of children

#### kay123

I'm trying to figure out this problem but i keep getting stuck.

The problem statement, all variables and given/known data

A woman wants to have a 95% chance for a least a one boy and at least one girl. What is the minimum number of children that she should plan to have? Assume that the event that a child is a girl and a boy is equiprobable and independent of the gender of the other children born in the family.

Relevant equations

So i know you should use Pr(K = k) = (n\choose k)p^k(1-p)^(n-k)

The attempt at a solution

since the it's a 95% chance Pr(K=k)= .95
probability of a boy or girl is 50% so it's .5

.95= (n\choose k).5^k(1-.5)^(n-k)
but then how would you solve or find what n and k is?
Am i missing something here?

Can anyone help! thank you in advance.

#### bpet

A woman wants to have a 95% chance for a least a one boy and at least one girl.
In other words the probability of n children being either all boys or all girls is less than 5%.

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving