Math  /  Data & Statistics

QuestionAn experiment consists of rolling two fair (not weighted) dice and adding the dots on the two sides facing up. Each die has the number 1 on two opposite faces, the number 2 on tw opposite faces, and the number 3 on two opposite faces. Compute the probability of obtaining the indicated sum.
Sum of 2
The probability of getting a sum of 2 is \square (Type an integer or a simplified fraction.)

Studdy Solution

STEP 1

1. Each die has three numbers: 1, 2, and 3, each appearing on two opposite faces.
2. The dice are fair, meaning each face has an equal probability of landing face up.
3. We are interested in the probability of the sum of the numbers on the two dice being 2.

STEP 2

1. Determine the total number of possible outcomes when rolling two dice.
2. Identify the outcomes that result in a sum of 2.
3. Calculate the probability of obtaining a sum of 2.

STEP 3

Determine the total number of possible outcomes when rolling two dice.
Each die has 3 different numbers, and each roll is independent. Therefore, the total number of outcomes is:
3×3=9 3 \times 3 = 9

STEP 4

Identify the outcomes that result in a sum of 2.
The possible outcomes for each die are 1, 2, and 3. To get a sum of 2, both dice must show 1. Therefore, the only outcome is:
(1,1) (1, 1)

STEP 5

Calculate the probability of obtaining a sum of 2.
The number of favorable outcomes is 1 (from Step 2), and the total number of outcomes is 9 (from Step 1). Thus, the probability is:
19 \frac{1}{9}
The probability of getting a sum of 2 is:
19 \boxed{\frac{1}{9}}

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