Question

Suppose that the proportion of fatal single-car accidents that involve alcohol consumption on the part of the driver is 60%. If the records of fatal single-car accidents in a geographical area are examined, what is the probability that the third accident involving alcohol consumption on the part of the driver is found in the eighth record examined? What type of distribution and what's the answer?

Answer 1

This is a negative binomial distribution

p = 0.6

k = 3

n = 8

P(3rd accident involving alcohol consumption is found in the 8th record) = P(2 out 7 accident involving alcohol consumption) * p

                                     = 7C2 * 0.6² * (1 - 0.6)^7-2 * 0.6

                                     = 0.0464