Question

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 7 girls? 

at most 7 girls?

Answer 1

Here, n = 8, p = 0.5, (1 - p) = 0.5 and x = 7
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 7).
P(X >= 7) = (8C7 * 0.5^7 * 0.5^1) + (8C8 * 0.5^8 * 0.5^0)
P(X >= 7) = 0.031 + 0.004
P(X >= 7) = 0.035

Here, n = 8, p = 0.5, (1 - p) = 0.5 and x = 7
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 7).
P(X <= 7) = (8C0 * 0.5^0 * 0.5^8) + (8C1 * 0.5^1 * 0.5^7) + (8C2 * 0.5^2 * 0.5^6) + (8C3 * 0.5^3 * 0.5^5) + (8C4 * 0.5^4 * 0.5^4) + (8C5 * 0.5^5 * 0.5^3) + (8C6 * 0.5^6 * 0.5^2) + (8C7 * 0.5^7 * 0.5^1)
P(X <= 7) = 0.004 + 0.031 + 0.109 + 0.219 + 0.273 + 0.219 + 0.109 + 0.031
P(X <= 7) = 0.995