Question

Corbin is playing a board game that requires rolling two number cubes to move a game piece. he needs to roll a sum of six on his first turn and then a sum of 10 on his second turn to land on the next two bonus spaces. what is the probability that corbin will roll a sum of six and then a sum of 10 on his next two turns.

Answer 1

To roll a sum of six ant then a sum of 10 on his next two turns are independent events, so the probabiliity of it is the product of the probability of the two separate events.

A) The probability of rolling a sum of six determined in this way:

1) Events that result in a sum of six points:
 
1 and 5,
2 and 4,
3 and 3,
4 and 2,
5 and 1

=> 5 ways of having a sum of six.

2) Total number of possibilities = 6*6 = 36

3) Probability = positive events /  total number of events = 5/36

B) The probability of rolling a sum of 10 is determined in this way:

1) Events that result in a sum of 10 points

4+6,
5+5,
6+4

Number of positive events: 3.

2) Total number of events: 6*6 = 36

3) Probability = positive events / total events = 3/36 = 1/12

C) Combined probability = (5/36) * (1/12) = 5/432 = 0.01157

Answer: 5/432 = 0.01157