Question

Business Man Goes To Hotels X. Y Z 20% 50% 30% Of Time Respectively. It Is Known That 5%, 4%, 8% Of The Rooms In The X Y Z Halts Have Faulty Plumbing
(a) Find The Probability That The Business Man Goes To The Whole With Faulty Plumbing
(b) What Is The Probability That A Business Man's Room Having Faulty Plumbing Is Assigned To Hotel Z?

Answer 1

Answer:

4/9

Step-by-step explanation:

Step 1:

The probability that the businessman goes to hotel X is P(X) = 0.2

The probability that the businessman goes to hotel Y is P(Y) = 0.5

The probability that the businessman goes to hotel Z is P (Z) = 0.3

Step 2:

Suppose A is the event of all the faulty plumbings, then it results in

P (A/X) = 0.05, P (A/Y) = 0.04 and P (A/Z) = 0.08.

Step 3:

The Probability that faulty plumbing is assigned to hotel Z is P (Z/A)

P(Z/A) = ( P(Z)∗P(A/Z) ) / ( P(X)∗P(A/X)+P(Y)∗P(A/Y)+P(Z)∗P(A/Z) )

= 0.3∗0.08 / 0.2∗0.05+0.5∗0.04+0.3∗0.08

= 0.024/ 0.1+0.02+0.024

= 0.024/0.054

= 24/54

= 4/9

Hence, the Probability that faulty plumbing is assigned to hotel Z is 4/9 .

Helpfully....

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