Shipments of raw materials are on time with probability 0.9. Find the probability that exactly one...

Shipments of raw materials are on time with probability 0.9.

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

r.v. X=
X~
P(X?

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

Solutions

Expert Solution

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

orchestra answered 1 year ago

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