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.
So, would these be correct?
a. 0.389
b.0.167
if you list the 36 possible outcomes, you can easily count the the relevant ones
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.