Craps Conditional Probability

The most complicated probability is the one that you asked - the probability that a 7 doesn't occur before any other number. It involves 1023 terms. Fortunately, it is the last term that the program computes, so all I had to do to get your answer was to have the program output this final probability. Condititional probability of A given B: P(AjB) = P(A B) P(B) It is also useful to think of this formula in a di erent way: we can write P(A B) = P(AjB)P(B) that is to compute the probability that both A and B occurs can be computed as the probability that B occurs time the conditional probability that A occurs given B. You can also solve this by going through the formula for conditional probability. To be honest I always have to look it up (check wikipedia for conditional probability), but you will end up dividing 1/20 by 10/20 and get 1/10. (d) The probability that a bettor rolls an 8 on the first roll and then wins is given by P(8)P(8 7 or 8). Show that this probability is (5/36)(5/11). (e) Show that the total probability that a bettor wins in the game of craps is 0.49293. Conditional probability is one way to do that, and conditional probability has very nice philosophical interpretations, but it fits into this more general scheme of “decomposing” events and variables into components. The usual way to break up a set into pieces is via a partition. Recall the following set-theoretic definition.

1. Craps Conditional Probability Definition
2. Craps Probabilities

Hey Wizard,
I'm a CJ/CIS major working in a Math department, and I've been asked to convert an open ended question test to multiple choice test. I found your site 'The Wizard of Odds', and was directed here to ask my question. What is the probability of rolling a 2 given your roll only being even, when rolling a 20 sided die? Thank you for your help.
-R

I know what you probably meant, but you actually need to specify what's on the 20-sided die. If it's 10 through 200 in increments of 10, the probability is zero.
Under the assumption that the d20 contains integers 1..20, here are the answers I'd list on a four-choice pick:
a) 1/2
b) 1/5
c) 1/10
d) 1/20
Edit: What's a 'CJ' major?

I know what you probably meant, but you actually need to specify what's on the 20-sided die. If it's 10 through 200 in increments of 10, the probability is zero.
Under the assumption that the d20 contains integers 1..20, here are the answers I'd list on a four-choice pick:
a) 1/2
b) 1/5
c) 1/10
d) 1/20
Edit: What's a 'CJ' major?

Funny, I read it differently for the same reason. I 'decided' the question stipulated the 20 sides were numbered 2 thru 20, evens only, with 2 identical sides per number, before I read ME's answer. Be interested to see the clarification.
I'm guessing 'Criminal Justice/Crime Scene Investigation' for the major.

If you're saying 'I've got a d20. The next roll will be an even number. What are the odds of that number being a 2?' Then I'd have to say the odds are 1 in 10. But how does one guarantee that no odd number will be rolled?

It's a conditional probability problem. It's guaranteed because the question says it's guaranteed. It's a math question, not a physics question.Designing multiple-choice tests is one of my favorite things to do. I see this question, and all I think is 'gosh, i wonder how they're doing answer placement. Is it randomized? Rotated? both?'

Craps Conditional Probability Definition

My HS world geography teacher was a sadistic guy. He put patterns into all his tests, but he also rotated the correct answers. So my 100% score could go a,b,c,d,a,b,c,d... while my friend could have the same answers but need to respond d,c,b,a,d,c,b,a... Made colluding and/or selling answers a real pain.

CJ - Criminal Justice
The numbers on the 20 sided dice are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. If this reply sounds smartalically, I appologize. I don't really understand what you mean needing to 'specify what's on the 20-sided die.' Anyhow, which is the answer; a, b, c, or d?

There are 10 even numbers. If you know for sure that it is even, then the answer is 1/10.
You can also solve this by going through the formula for conditional probability. To be honest I always have to look it up (check wikipedia for conditional probability), but you will end up dividing 1/20 by 10/20 and get 1/10.

Craps Probabilities