Question

4. The probability that there is no accident at a certain busy intersection is 95 % on any given day, independently of the other days a) (5 points) Find the probability that there will be no accidents at this intersection during the aext 7 days b) (5 points) Find the probability that next September (which has 30 days) there will be exactly 2 days with accidents. e) (5 points) Find the probability that there is no accident during the next 4 days, but there is at. least one by the end of the 10th day. d) (5 points) Find the expected number of days until the third accident. 5

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x

P(no accident on a day), p = 0.95

q = 1 - p = 0.05

a) P(no accident in next 7 days) = 0.95⁷

= 0.6983

b) P(exactly 2 days with accident in next September) = 30C2 x 0.95²⁸ x 0.05²

= 0.2586

c) P(no accident in first 4 days but at least one accident by end of 10th day) = 0.95⁴ x (1 - 0.95⁶)

= 0.2158

d) Mean = np = 3

n x 0.05 = 3

n = 3/0.05

n = 60 days