Question

. If two dice are thrown simultaneously, what is the probability of obtaining:

a) a double b) a prime number as sum of both dice c) at least one 4?​

Answer 1

Note: Total possible combinations are 36.

1) For double, (1,2) or (2,1) , (2,4) or (4,2) and (3,6) or (6,3). So, probability is 6/36= 1/6.

2) For getting prime sum,

it should be 2,3,5,7 or 11.

2 - 1 result (1,1)

3 - 2 result (1,2) and (2,1)

5 - 4 results (1,4),(2,3) and (3,2),(4,1)

7 - 6 results (1,6),(6,1),(2,5),(5,2),(3,4),(4,3)

11 - 2 results (5,6), (6,5)

Total = 15 results

Answer = 15/36 = 5/12

3) At least one 4 means 4 on first dice or on 2nd dice, so 11 results are possible.

(1,4),(2,4),(3,4),(4,4),(54),(6,4) and

(4,1),(4,2),(4,3),(4,5),(4,6)

Answer= 11/36.