please show steps and equations used Question 4. [6 Marks] A large industrial fi

Question

please show steps and equations used

Question 4. [6 Marks] A large industrial firm uses three local motels to provide overnight accom modations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the Ramada Inn, 50% at the Sheraton, and 30% at the Lakeview Motor Lodge. If the in 8% of the rooms at the Lakeview Motor Lodge, what is the probability that a) 3 marks] a client will be assigned a room with faulty plumbing? b) 3 marks] a person with a room having faulty plumbing was assigned accommodations at the Lakeview Motor Lodge?

Explanation / Answer

R stands for Ramada Inn

S stands for Sheraton

H stands for Holiday Inn

F stands for faulty plumbing

P(R) = 0.2

P(S) = 0.5

P(H) = 0.3

P(F | R) = 0.05

P(F | S) = 0.04

P(F | H) = 0.08

a) probability that A client will be assigned a room with faulty plumbing = P(F)

P(F) = P(R) * P(F | R) + P(S) * P(F | S) + P(H) * P(F | H)

        = 0.2 * 0.05 + 0.5 * 0.04 + 0.3 * 0.08

        = 0.054 (ans)

b) P(H | F) = P(H) * P(F | H) / P(F)

                  = 0.3 * 0.08 / 0.054

                  = 0.444 (ans)

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