# Thread: Probability questions

1. ## Probability questions

(1) If A and B are equiprobable outcomes and |B|=100, explain using a Venn Diagram why P(A) <= P(B).

(2) Three indistinguishable (fair) dice are thrown simultaneously at random. Find the probability that the sum of the three dice is less than six and that no two dice show the same face (the same number.)

For (2), I get 0. Is this correct?

Not sure what to do for (1). Any help?

2. Originally Posted by BrownianMan
(1) If A and B are equiprobable outcomes and |B|=100, explain using a Venn Diagram why P(A) <= P(B).

(2) Three indistinguishable (fair) dice are thrown simultaneously at random. Find the probability that the sum of the three dice is less than six and that no two dice show the same face (the same number.)

For (2), I get 0. Is this correct?

Not sure what to do for (1). Any help?
(1) If A and B are equiprobable then surely Pr(A) = Pr(B) by definition!

(2) No. I suggest you start by listing the favourable outcomes eg. (1, 2, 3), ......

3. It says less than 6 though, not less than or equal to 6. So (1,2,3) shouldn't be included. No?

4. If you mean "Find Pr(<6) and Pr(Different faces)" then the answer is 0.

First you can discard 4,5 and 6. Of the remaining outcomes the only different ones are 3,2 and 1 in each of the permutations. Since this adds up to 6 it doesn't satisfy the condition of being less than 6.

Thus it's impossible hence 0

5. That's how i interpret it. Less than 6, (<6).

6. Originally Posted by BrownianMan
It says less than 6 though, not less than or equal to 6. So (1,2,3) shouldn't be included. No?
You are correct. My mistake.