Probability with AND

Question

You want to find the probability of rolling a sum of 12 on two dice and then rolling a sum of 4 on the next roll.

Calculate the probability.

(Round to three decimal places.)

Answer 1

There are 6 sides on each die, so there are 36 different combinations that can occur when two dice are thrown (though of course some of them add up to the same number).

 

The only way to get 12 is with a 6 and a 6.  So the probability of getting 12 on the first roll is 1/36.

 

There are 3 ways to get a 4:  1/3, 2/2, 3/1.  So the probability of getting a 4 on the second roll is 3/36 or 1/12.

 

So the probability of both events happening is 1/36 * 1/12 = 0.002