a number cube is rolled twice. what is the probability of rolling an odd number on the first roll and a multiple of three on the second roll?
The probability of an odd number (1,3 or 5) on the first roll is 3/6=1/2
For the second roll, to get a multiple of three (3 or 6) the probability is 2/6=1/3
The two rolls are independent.
So the probability of succeeding both events is (1/2)*(1/3)=1/6
To find the probability of rolling an odd number on the first roll and a multiple of three on the second roll of a number cube, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes:
For the first roll, there are 3 odd numbers on a number cube (1, 3, and 5), and for the second roll, there are 2 numbers (3 and 6) that are multiples of three.
Therefore, the number of favorable outcomes is 3 × 2 = 6.
Step 2: Determine the total number of possible outcomes:
When rolling a number cube, there are 6 possible outcomes, as there are six faces on a cube.
Step 3: Calculate the probability:
To find the probability, divide the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 6 / 6 = 1
Therefore, the probability of rolling an odd number on the first roll and a multiple of three on the second roll of a number cube is 1, or 100%.
To find the probability of rolling an odd number on the first roll and a multiple of three on the second roll, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes:
- When rolling a number cube, there are 6 possible outcomes (numbers 1-6).
- Out of these 6 possible outcomes, 3 are odd numbers (1, 3, and 5) and 2 are multiples of three (3 and 6).
- Therefore, the number of favorable outcomes is 3 (odd numbers) * 2 (multiples of three) = 6.
Step 2: Determine the total number of possible outcomes:
- When rolling a number cube twice, each roll has 6 possible outcomes.
- Since we are considering the outcomes for both rolls together, we multiply the number of outcomes for each roll: 6 * 6 = 36.
Step 3: Calculate the probability:
- The probability is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
- Therefore, the probability of rolling an odd number on the first roll and a multiple of three on the second roll is 6 (favorable outcomes) / 36 (total outcomes).
- Simplifying this fraction, we get 1/6 as the probability.
So, the probability of rolling an odd number on the first roll and a multiple of three on the second roll is 1/6.