Question

Assume there are 11 voting districts in the county.  Polly Tician is running for office. She figures she must win at least 7 of the districts to win the election.  If she has an equal chance of 60% to win any one district, what are her chances of winning the election?

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Answer 1

53.3%

Explanation:

Here we will use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

In this case, n = 11, r ≥ 7, p = 0.6, and q = 0.4.

P = ₁₁C₇ (0.6)⁷ (0.4)⁴ + ₁₁C₈ (0.6)⁸ (0.4)³ + ₁₁C₉ (0.6)⁹ (0.4)² + ₁₁C₁₀ (0.6)¹⁰ (0.4)¹ + ₁₁C₁₁ (0.6)¹¹ (0.4)⁰

P = 0.236 + 0.177 + 0.089 + 0.027 + 0.004

P = 0.533