Question

# The Jones family was one of the first to come to the U.S. They had 5...

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

at least 2 girls?

at most 4 girls?

a)

Here, n = 5, p = 0.5, (1 - p) = 0.5 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X >= 2).
P(X >= 2) = (5C2 * 0.5^2 * 0.5^3) + (5C3 * 0.5^3 * 0.5^2) + (5C4 * 0.5^4 * 0.5^1) + (5C5 * 0.5^5 * 0.5^0)
P(X >= 2) = 0.3125 + 0.3125 + 0.1563 + 0.0313
P(X >= 2) = 0.8126

b)

Here, n = 5, p = 0.5, (1 - p) = 0.5 and x = 4
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 4).
P(X <= 4) = (5C0 * 0.5^0 * 0.5^5) + (5C1 * 0.5^1 * 0.5^4) + (5C2 * 0.5^2 * 0.5^3) + (5C3 * 0.5^3 * 0.5^2) + (5C4 * 0.5^4 * 0.5^1)
P(X <= 4) = 0.0313 + 0.1563 + 0.3125 + 0.3125 + 0.1563
P(X <= 4) = 0.9689

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