Thread: how to compute this probability?

Hi,
Here is problem.
Mr.X manages two auto parts stores,because he orders parts for both stores from the same supplier, he finds that if he runs out of a particular part at east store, he is usually out of the same part at the west store. Specifically 72% of the time that east store ran out of the KG—3 muffer so did the west store. If the probability of running out of this muffer at east store is 0.2 what is the probability of being out of the muffer at both the stores?
What information is needed to decide the probability of being out of the muffer at west store?

Hi Vinod!

The multiplication rule for probabilities is:
P(A and B) = P(A | B) P(B)

Say E is the event that the east store runs out, and W is the event that the west store runs out.

Can you write your facts as probabilities and apply the multiplication rule?

Originally Posted by ILikeSerena

Hi Vinod!

The multiplication rule for probabilities is:
P(A and B) = P(A | B) P(B)

Say E is the event that the east store runs out, and W is the event that the west store runs out.

Can you write your facts as probabilities and apply the multiplication rule?

In the problem, P(W|E) is not given. P(W|E) is said to be the conditional probability of the occurrence of event W,under the condition that event E has already occurred.

event E=east store runs out of the KG—3 mutter
event W= west store runs out of the KG—3 muffer

Hence I cannot apply the multiplication rule here.

Originally Posted by Vinod

Mr.X manages two auto parts stores,because he orders parts for both stores from the same supplier, he finds that if he runs out of a particular part at east store, he is usually out of the same part at the west store. Specifically 72% of the time that east store ran out of the KG—3 muffer so did the west store.

Originally Posted by Vinod

In the problem, P(W|E) is not given. P(W|E) is said to be the conditional probability of the occurrence of event W,under the condition that event E has already occurred.

But surely it is given.

Originally Posted by Plato

But surely it is given.

A little bit of help is required to understand the meaning of blue coloured sentence in the problem.wording of the sentence is little bit difficult to understand for me.
Thanks.

he's trying to get you to think.basically what he wants you to notice is that P(W|E) is given in the sentence: "Specifically 72% of the time that east store ran out of the KG—3 muffer so did the west store."

Plato,sorry for ruining your intentions!

Originally Posted by anonimnystefy

he's trying to get you to think.basically what he wants you to notice is that P(W|E) is given in the sentence: "Specifically 72% of the time that east store ran out of the KG—3 muffer so did the west store."

Plato,sorry for ruining your intentions!

So the probability of being out of the muffer at both the stores is = 0.72*0.2=0.144 .

Am i right?
Verify the answer because answer is not given in the questions paper set.

hi Vinod

yes,i think that should be right

Originally Posted by Vinod

So the probability of being out of the muffer at both the stores is = 0.72*0.2=0.144 .

Am i right?
Verify the answer because answer is not given in the questions paper set.

Yep. That's it! :-)