# Probability questions

• Sep 27th 2010, 04:51 PM
BrownianMan
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?
• Sep 27th 2010, 07:53 PM
mr fantastic
Quote:

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), ......
• Sep 28th 2010, 11:04 AM
BrownianMan
It says less than 6 though, not less than or equal to 6. So (1,2,3) shouldn't be included. No?
• Sep 28th 2010, 11:47 AM
e^(i*pi)
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
• Sep 28th 2010, 12:50 PM
BrownianMan
That's how i interpret it. Less than 6, (<6).
• Sep 28th 2010, 02:45 PM
mr fantastic
Quote:

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.