It is assume that when she children are born they are equally likely to be boys or girls what is the probability that a family contain four children conthree boys and one girl

1 answer

Based on the assumption that the probability of having a boy or a girl is the same, we can use the concept of binomial probability to calculate the probability of a family having three boys and one girl among four children.

The binomial probability formula is P(x) = (nCx) * (p^x) * ((1-p)^(n-x)), where:
- P(x) is the probability of getting exactly x successes in n trials
- n is the number of trials or children in this case (4)
- x is the desired number of successes or boys in this case (3)
- p is the probability of success or having a boy in this case (0.5)
- (nCx) is the combination formula (n! / (x! * (n-x)!))

Using this formula:
P(3 boys and 1 girl) = (4C3) * (0.5^3) * (0.5^(4-3))
= (4!/((3!)(4-3)!)) * (0.5^3) * (0.5)
= (4/((3!)(1!))) * (0.5^3) * 0.5
= (4) * (0.125) * 0.5
= 0.25

Therefore, the probability that a family with four children contains three boys and one girl is 0.25 or 25%.