SOLUTION: The Wilson family was one of the first to come to the U.S. They had 4 children. Assuming that the probability of a child being a girl is .5, find the probability that the Wilson fa

Algebra ->  Probability-and-statistics -> SOLUTION: The Wilson family was one of the first to come to the U.S. They had 4 children. Assuming that the probability of a child being a girl is .5, find the probability that the Wilson fa      Log On


   

Question 1145774: The Wilson family was one of the first to come to the U.S. They had 4 children. Assuming that the probability of a child being a girl is .5, find the probability that the Wilson family had at least 3 girls? At most 3 girls?
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

(a)  At given conditions, the probability to have at least 3 girls 


         P( to have at least 3 girls ) = P(3) + P(4) = C%5B4%5D%5E3%2A%281%2F2%29%5E3%2A%281%2F2%29 + C%5B4%5D%5E4%2A%281%2F2%29%5E4 = 4%2A%281%2F2%29%5E4 + 1%2A%281%2F2%29%5E4 = 5%2F16.    ANSWER



(b)  At given conditions, the probability to have at most 3 girls is equal

     to the COMPLEMENT of the probability to have 4 girls.


         P( to have at most 3 girls ) = 1 - P(4) = 1 - %281%2F2%29%5E4 = 1 - 1%2F2%5E4 = 1+-+1%2F16 = 15%2F16.   ANSWER