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 = [tex]\dfrac{1}{2}=0.5[/tex]
Now, the probability that there will be at least one girl will be:-
P(atleast one girl) = 1- P(all boys)
[tex]=1-(\dfrac{1}{2})^7\\\\=1-0.0078125\\\\=0.9921875[/tex]
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.
