Question

Suppose it is now 1:00 p.m. and the last ghost appearance (the 6th overall) was at 12:35 p.m. What is the probability that the 7th ghost will appear before 1:30 p.m., to the nearest three decimal places

Answer 1

Answer:

probability = 0.503

Step-by-step explanation:

given data

now = 1:00 p.m

last ghost appearance = 12:35 p.m

solution

we consider here Ghost appearances occur in house according to a Poisson process having a rate =  1.4 ghosts per hour

so time duration from 1:00 pm to 1:30 pm = 0.30 min = 0.5 hrs

and we take random variable denoting inter-arrival time  = Y

so here probability that the 7th ghost will appear before 1:30 p.m.  is as

probability = P(Y < 0.5)

probability = 1 - $e^{-1.4 \times 0.5)$

probability  = 1 - 0.497

probability = 0.503