Question

The probability of catching the flu this year is 0.15. Use the binomial model to find the probability that 2 out 5 members of the Dawson family get the flu this year

P(x)=[n!x!(n−x)!]pxqn−x


a.) 2.43%

b.) 10.7%

c.) 13.8%

d.) 23.7%

Answer 1

C) 13.8%

Explanation:

Probability of catching the flu = p = 0.15

Probability of not catching the flu = q = 1 - 0.15 = 0.85

n = 5

Using binomial expansion, we have

C(n,r)* p^r * q^n-r

Probability of having 2 out of 5 = p(x = 2)

p(x = 2) = C(5,2) (0.15)^2 (0.85)^3

= 10 * 0.0225 * 0.614125

= 0.138

= 0.138 * 100

= 13.8% (C)