Math Problem Statement

Two dice, one orange and one white, are thrown at the same time, and the numbers showing on the dice are added together. 3.1.1 Calculate the probability that the sum is 12. 3.1.2 Calculate the probability that the sum is greater than or equal to 13. 3.1.3 Calculate the probability that the sum is less than 9.

Solution

Let's analyze the problem step by step:

We are working with two six-sided dice, one orange and one white, each of which has numbers from 1 to 6. The problem asks us to compute three probabilities based on the sum of the dice.

3.1.1 Probability that the sum is 12

The only way to get a sum of 12 is if both dice show a 6. There is exactly 1 favorable outcome: (6, 6). The total number of outcomes when rolling two dice is 6×6=366 \times 6 = 36.

Thus, the probability P(sum=12)P(\text{sum} = 12) is: P(sum=12)=136P(\text{sum} = 12) = \frac{1}{36}

3.1.2 Probability that the sum is greater than or equal to 13

The maximum possible sum of two dice is 12 (which occurs with the combination (6, 6)), so there are no outcomes where the sum is 13 or greater.

Thus, the probability P(sum13)P(\text{sum} \geq 13) is: P(sum13)=0P(\text{sum} \geq 13) = 0

3.1.3 Probability that the sum is less than 9

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Math Problem Analysis

Mathematical Concepts

Probability
Combinatorics

Formulas

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Theorems

Basic Probability Theory

Suitable Grade Level

Grades 8-10