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The Wilson family had 8 children. Assuming that the probability of a child being a girl...

The Wilson family had 8 children. Assuming that the probability of a child being a girl is 0.5, find the probability that the Wilson family had: at least 3 girls? at most 3 girls? Round your answers to 4 decimal places.

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Answer #1

Given that, the Wilson family had 8 children. Assuming that the probabilitiy of a child being a girl is 0.5.

Let X be a number of girls among 8 children.

Here, X ~ Binomial (n = 8, p = 0.5)

a) We want to find, P(X ≥ 3)

P(X ≥ 3)

= 1 - P(X ≤ 2)

= 1 - [ P(X = 0) + P(X = 1) + P(X = 2) ]

= 1 - [ 0.0039 + 0.0312 + 0.1094 ]

= 1 - 0.1445

= 0.8555

Therefore, the probabilitiy that the Wilson family had at least 3 girls is 0.8555

b) We want to find, P(X ≤ 3)

(X ≤ 3)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 0.0039 + 0.0312 + 0.1094 + 0.2188

= 0.3633

Therefore, the probabilitiy that the Wilson family had at most 3 girls is 0.3633

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