Question

1 in 4 adults are on a diet. in a random sample of 10 adults, what is the probability that the number on a diet is exactly 4​

Answer 1

14.6%

Explanation:

Use binomial probability:

P = nCr pʳ (1−p)ⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

and p is the probability of success.

Here, n = 10, r = 4, and p = 1/4.

P = ₁₀C₄ (1/4)⁴ (1−1/4)¹⁰⁻⁴

P = 210 (1/4)⁴ (3/4)⁶

P ≈ 0.146

There is an approximate 14.6% probability that exactly 4 of the 10 adults are on a diet.