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# conditional prob

Posted on 2013-06-05
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Hi,

I know the answer but I cant work this out.  It should be a conditional prob question

10% diesel. When a customer buys super there is a 25% chance they will fill the tank.
diesel, 70% fill their tank.

Given that a car leaving the petrol station has a full tank, what is the probability that
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Question by:jagguy
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Expert Comment

First let me ask if I have the correct answer since you say you already know.  Is it 12% chance?

Let's say there are 10 people.

10 * 30% = 3 people buy super
10 * 10% = 1 person buys diesel

6 * 20% = 1.2 people that buy unleaded will fill their tank

1.2 / 10 = .12 (12%) probability that the car leaving will with a full tank will have unleaded.

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Expert Comment

Draw it out as a grid.

full         not full
super      .3*.25        .3*.75
diesel

Now fill out the rest of the table.

If you add up the first column, you will have the total probability of a full tank. What percent of that is from unleaded?
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LVL 27

Expert Comment

The best way to do these problems is to draw the full probability tree.

The top three-way branch is 30, 60, 10

Each of those branches twice into Fill/No_Fill

That gives you six possibilities on the bottom row.

Collect the Fill terms and scale the sum of the probabilities back to 100%.
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LVL 37

Expert Comment

pony10us, that is the chance that any car will leave with a full tank of unleaded.

Given that a car's tank is full, the probability that it is unleaded is between 40 and 50%

I know the exact answer, but I don't want to post it until the asker does.
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Accepted Solution

TommySzalapski earned 500 total points
Remember the probability of A given B is the probability that both are true divided by the probability that B is true

P(A|B) = P(A and B)/P(B)

So what is P(A and B) and what is P(B)?

Either the table or the tree will give you both.
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LVL 26

Expert Comment

Tommy,

Okay, I think I understand.  If I am correct then I may be closer to the answer.  I was only partially through the process apparently.

Been a long time since I did any math like this and it intrigued me.

:)
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Expert Comment

From a layman's approach -
The 120 unleaded customers fill up 24 times, the super customers 15 times, and the diesel customers 14 times. So a total of 53 customers have full tanks, 24 of which are unleaded.
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LVL 37

Expert Comment

Yes. That is precisely the same thing that the table or tree would get you, except they use 1 (100%) instead of 200.
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LVL 31

Expert Comment

Thanks, Tommy. I think it's just easier for us dummies to think in terms of 24, 15, and 14 people as opposed to .12, .075, and .07 people. :-)
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Author Comment

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Author Closing Comment

well done
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LVL 26

Expert Comment

jagguy

Exactly what I ended up with after Tommy corrected my logic.  :)

Thanks Tommy.

the formula I have on an excel spreadsheet is:

=(0.6*0.2)/((0.3*0.25)+(0.6*0.2)+(0.1*0.7))

I imagine there is a simpler method though.
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