What is the probability of each event?
a. rolling a sum of a prime number on one roll of two standard number cubes.
b. rolling a sum of 5 or a sum of 3 on one roll of two standard number cubes.
6 years ago
6 years ago
So, would these be correct?
a. 0.389
b.0.167
11 months ago
To calculate the probability of each event, let's break down the problem step by step.
a. Rolling a sum of a prime number on one roll of two standard number cubes:
To find the probability, we need to determine the total number of outcomes and the number of favorable outcomes.
1. Determine the total number of outcomes: When rolling two standard number cubes, each cube has six sides, numbered 1 to 6. Therefore, the total number of outcomes is 6 * 6 = 36.
2. Determine the number of favorable outcomes: We need to find the number of ways to get a sum of a prime number. Prime numbers between 2 and 12 are 2, 3, 5, 7, 11. Let's find all the possible combinations that yield these prime numbers:
- For 2: (1,1)
- For 3: (1,2), (2,1)
- For 5: (1,4), (2,3), (3,2), (4,1)
- For 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
- For 11: (5,6), (6,5)
So, the number of favorable outcomes is 2 (for the sum of 2), plus 2 (for the sum of 3), plus 4 (for the sum of 5), plus 6 (for the sum of 7), plus 2 (for the sum of 11), which equals 16.
3. Calculate the probability: Divide the number of favorable outcomes by the total number of outcomes to get the probability.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 16 / 36
Probability = 4 / 9
Therefore, the probability of rolling a sum of a prime number on one roll of two standard number cubes is 4/9.
b. Rolling a sum of 5 or a sum of 3 on one roll of two standard number cubes:
Similar to the previous question, we'll follow the same steps:
1. Determine the total number of outcomes: When rolling two standard number cubes, each cube has six sides, numbered 1 to 6. Therefore, the total number of outcomes is 6 * 6 = 36.
2. Determine the number of favorable outcomes: We need to find the number of ways to get a sum of 5 or a sum of 3.
- For the sum of 5: (1,4), (2,3), (3,2), (4,1)
- For the sum of 3: (1,2), (2,1)
So, the number of favorable outcomes is 4 (for the sum of 5) plus 2 (for the sum of 3), which equals 6.
3. Calculate the probability: Divide the number of favorable outcomes by the total number of outcomes to get the probability.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 6 / 36
Probability = 1 / 6
Therefore, the probability of rolling a sum of 5 or a sum of 3 on one roll of two standard number cubes is 1/6.