Two dice are thrown simultaneously.What is the probability of getting a pair of numbers whose ratio is in simplest form?5/921/3623/3611/18

To find the probability of getting a pair of numbers whose ratio is in simplest form when two dice are thrown simultaneously, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Step 1: Determine the total number of possible outcomes: When two dice are thrown simultaneously, each die has 6 possible outcomes (numbers 1 to 6). Since there are two dice, the total number of possible outcomes is 6 x 6 = 36.

Step 2: Determine the number of favorable outcomes: To find the number of favorable outcomes, we need to consider the pairs of numbers whose ratio is in simplest form. Let's list them: 1/1, 2/1, 3/1, 4/1, 5/1, 6/1 2/2, 3/2, 4/2, 5/2, 6/2 3/3, 4/3, 5/3, 6/3 4/4, 5/4, 6/4 5/5, 6/5 6/6

Counting these pairs, we find that there are 21 favorable outcomes.

Step 3: Calculate the probability: The probability is given by the number of favorable outcomes divided by the total number of possible outcomes. Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 21 / 36

Simplifying the fraction, we get: Probability = 7 / 12

Therefore, the probability of getting a pair of numbers whose ratio is in simplest form when two dice are thrown simultaneously is 7/12.