Question

The probability of an adverse reaction to a pneumonia shot is 0.30. Pneumonia shots are given to a group of 12 people. What is the probability that two or more of them will have an adverse reaction to the pneumonia shot? A. 0.9149 B. 0.8923 C. 08722 D. 0.5211

Answer 1

Let p = probability of an adverse reaction to a pneumonia shot = 0.30

we have n = 12

We asked P( X 2) = 1 - P( X 1)

= 1 - [ P( X = 0) + P( X = 1)]

Using binomial probability

P( X = 0) = 12!/0!*12! *(0.30)0*(0.70)12 = 0.0138

P(X = 1) = 12!/1!*11! *(0.30)1* (0.70)11 = 0.0712

P( X 2) = 1 - (0.0138+0.0712)

P( X 2) = 0.9149