Question

A 2005 Gallup Poll found that 7% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other.

Calculate the probability that at least one of them suffers from arachnophobia.

Answer 1

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).

Given:

n = 10, r ≥ 1, p = 0.07, q = 0.93

P(r ≥ 1) = 1 − P(0)

P(r ≥ 1) = 1 − ₁₀C₀ (0.07)⁰ (0.93)¹⁰⁻⁰

P(r ≥ 1) = 1 − (0.93)¹⁰

P(r ≥ 1) = 0.516

Explanation:

Answer 2

0.516

Explanation:

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).

Given:

n = 10, r ≥ 1, p = 0.07, q = 0.93

P(r ≥ 1) = 1 − P(0)

P(r ≥ 1) = 1 − ₁₀C₀ (0.07)⁰ (0.93)¹⁰⁻⁰

P(r ≥ 1) = 1 − (0.93)¹⁰

P(r ≥ 1) = 0.516