# Thread: how to compute this probability?

1. ## 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?

2. ## Re: how to compute this probability?

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?

3. ## Re: how to compute this probability?

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.

4. ## Re: how to compute this probability?

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.

5. ## Re: how to compute this probability?

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.

6. ## Re: how to compute this probability?

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."

7. ## Re: how to compute this probability?

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."

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.

8. ## Re: how to compute this probability?

hi Vinod

yes,i think that should be right

9. ## Re: how to compute this probability?

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! :-)