Two dice are thrown simultaneously. What is the probability that the sum of the

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Question: Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the dice is 7?

Options:

Correct Answer: 1/6

Solution:

Possible outcomes for sum = 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 outcomes. Total outcomes = 6 * 6 = 36. Probability = 6/36 = 1/6.

Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the dice is 7?

Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the dice is 7?

Step 1: Understand that we are throwing two dice, and each die has 6 faces numbered from 1 to 6.
Step 2: Calculate the total number of possible outcomes when throwing two dice. Since each die has 6 faces, the total outcomes are 6 (from the first die) multiplied by 6 (from the second die), which equals 36.
Step 3: Identify the specific outcomes where the sum of the numbers on the two dice equals 7. These outcomes are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
Step 4: Count the number of outcomes that give a sum of 7. There are 6 outcomes that result in a sum of 7.
Step 5: Calculate the probability of getting a sum of 7 by dividing the number of favorable outcomes (6) by the total number of outcomes (36). This gives us 6/36.
Step 6: Simplify the fraction 6/36 to get the final probability, which is 1/6.

Probability – Understanding the likelihood of an event occurring, calculated as the number of favorable outcomes divided by the total number of possible outcomes.
Combinatorics – The study of counting, arrangements, and combinations, particularly relevant in determining the total outcomes when rolling dice.