Question

If a couple plans to have 8 ​children, what is the probability that there will be at least one girl​? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will get at least one girl in 8 ​children?

Answer 1

It is given that getting boy or girl is equally likely. The chance of getting boy or girl on birth is 1/2

P(Boy) = P(Girl) =0.5

If a couple plans to have 8 children then probability of getting at least one girl is

P(Al least one girl out of 8 children) = 1 - P(No girl in 8 children)

= 1 - P( Getting all boys in 8 children)

= 1 - (0.5)^8

= 1 - 0.0039

P(At least one girl out of 8 children) = 0.9961

The probability of getting at least one girl out of 8 children is 0.9961.

The probability 0.9961 is high enough for the couple to be very confident that they will get at least one girl in 8 ​children