Math Is Fun Forum

Karn

Member

Registered: 2009-11-15

Posts: 14

Conditional probability

Urgent. Studying for a test however in this revision task I having trouble with the following questions.
Q.A normal six sided die is rolled twice and the scores obtained are added together.
   Event A is that of the first roll giving a 5
   Event B is that of the total being 10

Determine (a) P(B:A)  (b) P(A:B)

Event C is that of the first roll giving a 2
Event D is that of the total being 6

Determine (c) P(D:C)   (d) P(C:D)

Event E is that the first roll giving an odd number
Event F is that of giving the total being 5

determine (e) P(F:E)   (f) P(E:F)

Help is greatly appreciated

Thank you:)

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Conditional probability

Does P(B:A) mean given B is true, what is Probability of A being true?
Does P(A:B) mean given A is true, what is prob of B being true?

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igloo myrtilles fourmis

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Conditional probability

I've always written it the opposite of that way. But I also use a |.

ie., for me, P(A|B) means P(A), given B.

Since the questions are symmetric though, it doesn't matter too much. No matter how you interpret it, you'll give a set of correct answers.

The way to answer these questions is to work out the ways of both events happening, then divide by the ways of the given event happening.

For the first question, there is only one way of rolling a 5 with the first dice and totalling 10 - rolling two fives.

But there are 6 ways of rolling a 5 with the first:
(5,1); (5,2); (5,3); (5,4); (5,5); (5,6)

Therefore, P(B|A) is 1/6.

The second question has the same first half.
But this time we work out that there are 3 ways of rolling a 10 with both:
(4,6); (5,5); (6,4)

Therefore, P(A|B) is 1/3.

The other four are answered in much the same way.

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Why did the vector cross the road?
It wanted to be normal.