Question

A pair of dice are rolled​ 1,000 times with the following frequencies of​ outcomes:

Sum	2	3	4	5	6	7	8	9	10	11	12
Frequency	10	30	50	70	110	150	170	140	120	80	70

Use these frequencies to calculate the approximate empirical probabilities and odds for the events a. The sum is less than 3 or greater than 9.

b. The sum is even or exactly divisible by 5.

a. Probabilityequals = ___???

​(Type a​ decimal.)

Odds for = ____??

​(Type a fraction. Simplify your​ answer.)

b. Probabilityequals = ___???

​(Type a​ decimal.)

Odds for = ____??

​(Type a fraction. Simplify your​ answer.)

Answer 1

a) P(sum is less than 3 or greater than 9) = P(2) + P(10) + P(11) + P(12)

                                                                  = 10/1000 + 120/1000 + 80/1000 + 70/1000

                                                                  = 280/1000

                                                                  = 7/25

                                                                  = 0.28

Odds for = (7/25) / (1 - 7/25) = 7/18

b) P(sum is even of divisible by 5) = P(2) + P(4) + P(5) + P(6) + P(8) + P(10) + P(12)

                                                       = 10/1000 + 50/1000 + 70/1000 + 110/1000 + 170/1000 + 120/1000 + 70/1000

                                                       = 3/5

                                                       = 0.6

Odds for = (3/5) / (1 - 3/5) = 3/2