Probability

Question

Hazel is playing a game with two regular dice and needs to roll a sum of 9 at least once in the next 7 rolls in order to win. What is the probability that Hazel will win? Answer with a percentage rounded to the nearest tenth of a percent

Answer 1

1) Figure out the P(rolling a 9).

 

Total combinations of 2 dice rolls = 6*6 = 36

How many ways to roll a 9: 6-3, 3-6, 5-4, 4-5 (4 ways)

P(rolling a 9) = 4/36 = 1/9

 

2) Use the binomial distribution to solve.

 

P(rolling a 9 at least once in 7 tries)

= 1 - P(not rolling a 9 at all in 7 tries)

= 1 - [7C0 * (1/9)^0 * (8/9)^7]

= 1 - [1 * 1 * .438]

= 1 -.438

= .562