Question

The Wilson family had 9 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the wilson family had:

at least 7 girls?

Score on last attempt: 1/1) 1 out of 2 (parts: * 0/1, 1 out of 2 (parts: #0/1, Score in gradebook: 1/1) Reattempt last question below, or select another question The Wilson family had 9 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had: at least 7 girls? 91 at most 7 girls? .9805 Round your answers to 4 decimal places. Licens Points available on this attempt: 1.9 of original 2 Unlimited attempts. Score on last attempt: (0,1). Score in gradebook: (0,1), Out of: (1,1)

Answer 1

• Here number of children in the Wilson family, n = 9 is a given fixed number. • A child being a girl is not affected by whether other children are girls or boys, that is a randomly selected child being girl is independent. • Also each child is either a girl with probability, p=0.5 or a boy with probability, q=1-p=0.5 Therefore number of girl child in the Wilson family, X, has a binomial prob- ability distribution with parameters n=9, p=0.5 The pmf of X can be given as P(X = k) = (*)(0.5)*(0.5)9–k = ()(0.5) 9 k =0,1, 2, ..., 9 The probability that the Wilson family had at least 7 girls,

P(x > 7) = P(X = 7) + P(X = 8) + P(X = 9) = (?) (0.5) + (3) (0.5) + () (0.5) = [(>) + (%) + (%)] (0.5)9 = (36 +9+1) X (0.5) = 46 x (0.5) = 0.08984375 0.0898