(1 pt) A couple decided to have 5 children (a) What is the probability that they will have at least two boys? (b) W...

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Answer 1

Answer #1

a)
Here, n = 5, p = 0.5, (1 - p) = 0.5 and x = 1
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 1).
P(X <= 1) = (5C0 * 0.5^0 * 0.5^5) + (5C1 * 0.5^1 * 0.5^4)
P(X <= 1) = 0.0313 + 0.1563
P(X <= 1) = 0.1876

probability = 1 - 0.1876 = 0.8124

b)
P(All same gender) = 0.5^5 + 0.5^5 = 0.0625

Answer 2

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