- #1

newguy2

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This question has been driving me crazy.

A large industrial firm uses three local motels to provide overnight accommodations 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 Lakeview. What is the probability that:

P(R) = 'Probability of being assigned to Ramada' = 20% = .20

P(S) = 'Probability of being assigned to Sheraton' = 50% = .50

P(L) = 'Probability of being assigned to Lakeview' = 30% = .30

P(F) = 'The probability of faulty plumbing' = ?

P(F | R) = 'Given room is at Ramada, prob. of faulty plumbing' = 5% = .05

P(F | S) = 'Given room is at Sheraton ...' = 4% = .04

P(F | L) = 'Given room is at Lakeview ...' = 8% = .08

Right?

So...:

A) What is the probability that a client will be assigned a room with faulty plumbing?

P(F) = P(R)P(F|R) + P(S)P(F|S) + P(L)P(F|L) = .20*.05 + .50*.04 + .30*.08 = 5.4% = .054

This makes sense...ok..

But...

B) What is the probability that a person with a room having faulty plumbing was assigned accommodations at Lakeview?

P(L | F) is what we are looking for, yes?

P(L | F) = 'Prob. of being assigned to LakeView, given room has faulty plumbing"

Right?

P(L | F) = P(L n F) / P(F) = P(F | L) P(F) / P(F) = P(F | L)...? This answer is not correct... how come?

P(L | F) = P(L n F) / P(F) = P(L) P(F) / P(F) = P(L)...? This answer is also not correct...

P(L | P(F|L)) = P(L n [F | L]) / P(F | L) = P(L)P(F | L) / P(F | L) = P(L) Still incorrect answer...

But this works...?

P(L | F) = P(L) P(F | L) / P(F) = correct answer?Please clarify all this for me.. What is happening.

A large industrial firm uses three local motels to provide overnight accommodations 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 Lakeview. What is the probability that:

P(R) = 'Probability of being assigned to Ramada' = 20% = .20

P(S) = 'Probability of being assigned to Sheraton' = 50% = .50

P(L) = 'Probability of being assigned to Lakeview' = 30% = .30

P(F) = 'The probability of faulty plumbing' = ?

P(F | R) = 'Given room is at Ramada, prob. of faulty plumbing' = 5% = .05

P(F | S) = 'Given room is at Sheraton ...' = 4% = .04

P(F | L) = 'Given room is at Lakeview ...' = 8% = .08

Right?

So...:

A) What is the probability that a client will be assigned a room with faulty plumbing?

P(F) = P(R)P(F|R) + P(S)P(F|S) + P(L)P(F|L) = .20*.05 + .50*.04 + .30*.08 = 5.4% = .054

This makes sense...ok..

But...

B) What is the probability that a person with a room having faulty plumbing was assigned accommodations at Lakeview?

P(L | F) is what we are looking for, yes?

P(L | F) = 'Prob. of being assigned to LakeView, given room has faulty plumbing"

Right?

P(L | F) = P(L n F) / P(F) = P(F | L) P(F) / P(F) = P(F | L)...? This answer is not correct... how come?

P(L | F) = P(L n F) / P(F) = P(L) P(F) / P(F) = P(L)...? This answer is also not correct...

P(L | P(F|L)) = P(L n [F | L]) / P(F | L) = P(L)P(F | L) / P(F | L) = P(L) Still incorrect answer...

But this works...?

P(L | F) = P(L) P(F | L) / P(F) = correct answer?Please clarify all this for me.. What is happening.

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