Please show every step amd calculation If you roll two fair

Please show every step amd calculation

If you roll two fair dice, what is the probability of getting:

(a) Two sixes?

(b) two numbers that sum to seven?

Answers:

(a) Total number of possible outcomes if we roll two dice = 6*6 = 36

Probability of getting two sixes = 1, that is (6, 6)

Therefore probability of getting two sixes = Number of favorable outcomes / Total number of possible outcomes

= 1/36

(b) Let E = event of getting a sum of 7. The number which is a sum of 7 will be E = [(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)] = 6

Therefore, probability of getting ‘a sum of 7’

P(E) = Number of favorable outcomes / Total number of possible outcomes

= 6/36 = 1/6