Question

If a couple plans to have 7 ​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 7 ​children?

Answer 1

Answer with explanation:

Given : The number of children a family plans to have = 7

If the boys and girls are equally likely, then the probability of getting a girl = probability of getting boy = $\dfrac{1}{2}=0.5$

Now, the probability  that there will be at least one girl​ will be:-

P(atleast one girl) = 1- P(all boys)

$=1-(\dfrac{1}{2})^7\\\\=1-0.0078125\\\\=0.9921875$

Hence, the probability that there will be at least one girl​ = 0.9921875

Since ,0.9921875 > 0.5  

It means the event is likely to happen.   [∵Any event E is likely to happen if P(E)>0.5]

Therefore, the probability is high enough for the couple to be very confident that they will get at least one girl in 7 ​children.