Question

Sean is playing a board game. To win he needs to roll a sum of 10 or more with a pair of dice on his next turn. There are 11 possible sums when you roll 2 dice and 3 of these outcomes will result in him winning this game. Sean therefore says that the probability that he will win the game is 3/11. Explain the mistake in Sean's thinking.

Answer 1

Answer: 1/6

Explanation:

Two fair dice is rolled once,

To win sum of the two dice should equal 10 or more

To get a sum equal 10 or more,

The total possible outcome when two dice is rolled once = 6^2 = 36

Sample space is attached below

Total required outcome to win (probability of having a sum of 10 or more)

n(sum of 10 or more) = 6

Therefore, probability of winning equals :

P(winning) = (Total required outcome / Total possible outcomes)

P(winning) = n(sum of 10 or more) / total possible outcomes

P(winning) = 6/36 = 1/6