Question

1. Shipments of raw materials are on time with probability 0.9.

1. Find the probability that exactly one shipment out of the next five is LATE.

• r.v. X=
• X~
• P(X?

2. Find the probability that the fifth shipment is the first LATE one.

Answer 1

Probability that a shipment is on time = 0.9

Probability that a shipment is late: p = 1- 0.9 = 0.1

probability that exactly one shipment out of the next five is LATE

X : Number of LATE shipment

Number of shipments : n = 5

Probability that a shipment is late: p = 0.1

q = 1-p = 1-0.1 =0.9

X is Binomial distribution with n= 5 and p =0.1

Probability mass function of X ; Probability of 'r' shipments are late out of 5 shipments

probability that exactly one shipment out of the next five is LATE = P(X=1)

probability that exactly one shipment out of the next five is LATE = 0.32805

b. probability that the fifth shipment is the first LATE one

Event of fifth shipment is the first LATE one i.e

First 4 shipments are in time and fifth shipment is late

Probability of first four shipments are in time = 0.9 x 0.9 x 0.9 x 0.9 = 0.6561

Probability that 5th shipment is late = 0.1

Probability that the fifth shipment is the first LATE one = Probability of first four shipments are in time x Probability that 5th shipment is late = 0.6561 x 0.1 = 0.06561

Probability that the fifth shipment is the first LATE one = 0.06561