Probability / Stats

Question

If you roll a pair of dice 4 times, what is the probability of not rolling any doubles?

One game might involve 150 rolls of the pair of dice, what is the expected value for the number of doubles in 150 rolls of the dice?

Answer 1

When you roll 2 dice there are 36 possible outcomes 6 of which are doubles and 30 which are not so the probability of rolling a non double is 30/36 or 5/6 on each roll so the probability of this happening 4 times in a row is (5/6)^4=.4822

Since doubles occur 1/6th of the time you would expect 150 x 1/6=25 doubles