Question

A pair of dice is rolled, and the numbers showing are observed. Find the probability that the two dice show doubles (the same number).

Answer 1

To find the probability that two dice show doubles (the same number), we need to determine the number of favorable outcomes (when the two dice show the same number) and the total number of possible outcomes.

There are 6 possible outcomes for each die, ranging from 1 to 6. Since we have two dice, the total number of possible outcomes is 6 * 6 = 36.

Now, let's determine the number of favorable outcomes, which is when the two dice show the same number (doubles). There are 6 possible doubles: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6).

Therefore, the number of favorable outcomes is 6.

To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 36
= 1 / 6

Hence, the probability that two dice show doubles is 1/6 or approximately 0.1667.

Answer 2

The probability of rolling doubles with a pair of dice is 1/6.

Step-by-step explanation:

To find the probability that the two dice show doubles (the same number), we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.

There are six possible outcomes for each dice roll, and there are six pairs of doubles (1-1, 2-2, 3-3, 4-4, 5-5, 6-6).

Therefore, the probability of rolling doubles is 6/36 or 1/6.