Answer :
To determine the probability that the sum of the numbers rolled on two number cubes (each numbered from 1 to 6) will be 5, follow these steps:
1. Understand the Scenario:
- Each cube has 6 sides.
- The total possible outcomes when rolling two cubes can be found by multiplying the number of sides on the first cube by the number of sides on the second cube.
- Therefore, we have [tex]\( 6 \times 6 = 36 \)[/tex] possible outcomes when rolling two cubes.
2. Identify Favorable Outcomes:
- We need to count the specific outcomes where the sum of the numbers on the two cubes equals 5.
- Let's list the pairs of numbers from each cube that sum to 5:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)
- There are 4 such pairs.
3. Calculate the Probability:
- The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
- In this case, the number of favorable outcomes is 4, and the total number of possible outcomes is 36.
4. Express the Probability:
- The probability [tex]\( P \)[/tex] can be computed as:
[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{36} \][/tex]
- Simplify this fraction:
[tex]\[ \frac{4}{36} = \frac{1}{9} \][/tex]
Given this, the correct answer to the question is:
[tex]\[ B \) \frac{1}{9} \][/tex]
1. Understand the Scenario:
- Each cube has 6 sides.
- The total possible outcomes when rolling two cubes can be found by multiplying the number of sides on the first cube by the number of sides on the second cube.
- Therefore, we have [tex]\( 6 \times 6 = 36 \)[/tex] possible outcomes when rolling two cubes.
2. Identify Favorable Outcomes:
- We need to count the specific outcomes where the sum of the numbers on the two cubes equals 5.
- Let's list the pairs of numbers from each cube that sum to 5:
- (1, 4)
- (2, 3)
- (3, 2)
- (4, 1)
- There are 4 such pairs.
3. Calculate the Probability:
- The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
- In this case, the number of favorable outcomes is 4, and the total number of possible outcomes is 36.
4. Express the Probability:
- The probability [tex]\( P \)[/tex] can be computed as:
[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{4}{36} \][/tex]
- Simplify this fraction:
[tex]\[ \frac{4}{36} = \frac{1}{9} \][/tex]
Given this, the correct answer to the question is:
[tex]\[ B \) \frac{1}{9} \][/tex]
