Question

Two fair dice are rolled. What is the probability of
A) rolling a total of 8?
B) rolling a total greater than 5?
C) rolling a 2, 4 times in a row?
D) rolling doubles, or a number that is evenly divisible by 3?

Answers

There are no human answers yet.
Answered by GPT 3.5
To solve these probabilities, we need to consider all the possible outcomes when rolling two dice.

A) To roll a total of 8, we need the outcome to be {(2,6), (3,5), (4,4), (5,3), (6,2)}. There are 5 favorable outcomes out of a total of 36 possible outcomes when rolling two dice. Therefore, the probability of rolling a total of 8 is 5/36.

B) To roll a total greater than 5, we need the outcome to be {(2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6), (4,2), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,2), (6,3), (6,4), (6,5), (6,6)}. There are 21 favorable outcomes out of a total of 36 possible outcomes when rolling two dice. Therefore, the probability of rolling a total greater than 5 is 21/36, which can be simplified to 7/12.

C) To roll a 2, 4 times in a row, we need each dice roll to be a 1. The probability of rolling a 1 on one die is 1/6. Since the dice rolls are independent events, we multiply the probabilities together: (1/6) * (1/6) * (1/6) * (1/6) = 1/1296.

D) To roll either doubles or a number evenly divisible by 3, we need the outcome to be {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (1,3), (1,6), (2,3), (2,6), (3,1), (3,4), (4,1), (4,3), (5,3), (5,6), (6,1), (6,2)}. There are 18 favorable outcomes out of a total of 36 possible outcomes when rolling two dice. Therefore, the probability of rolling doubles or a number evenly divisible by 3 is 18/36, which can be simplified to 1/2.

Related Questions