If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd.
To find the probability of rolling a 4 given that the number rolled is odd, we first need to determine the probability of rolling an odd number.
Step 1: Determine the probability of rolling an odd number:
A fair die has 6 equally likely outcomes, which are the numbers 1, 2, 3, 4, 5, and 6. Out of these 6 outcomes, 3 are odd numbers (1, 3, and 5).
So, the probability of rolling an odd number is given by:
P(Odd) = Number of odd outcomes / Total number of outcomes
P(Odd) = 3 / 6
P(Odd) = 1/2
Step 2: Determine the probability of rolling a 4 given that the number rolled is odd:
Now, we need to determine the probability of rolling a 4 given that the number rolled is odd. Since the die is fair, the probability of rolling a 4 is 1/6.
Step 3: Calculate the conditional probability:
The probability of rolling a 4 given that the number rolled is odd is given by:
P(4 | Odd) = Probability of rolling a 4 and the number rolled is odd / Probability of rolling an odd number
P(4 | Odd) = (1/6) / (1/2)
P(4 | Odd) = (1/6) * (2/1)
P(4 | Odd) = 2/6
P(4 | Odd) = 1/3
Therefore, the probability of rolling a 4 given that the number rolled is odd is 1/3.
To find the probability of rolling a 4 given that the number rolled is odd, we need to determine the favorable outcome and the total possible outcomes.
1. Determine the favorable outcome:
Since we know that the number rolled is odd, the possible outcomes are 1, 3, or 5. Out of these outcomes, only one of them is a 4. Therefore, the favorable outcome is 1.
2. Determine the total possible outcomes:
A fair die has six faces, numbered 1 through 6. Since the die is rolled once, the total possible outcomes are 6.
3. Calculate the probability:
The probability of an event is given by the ratio of the favorable outcomes to the total possible outcomes. In this case, the probability of rolling a 4 given that the number rolled is odd is:
P(4 | odd) = (Number of favorable outcomes) / (Number of total possible outcomes)
P(4 | odd) = 1/6
Therefore, the probability of rolling a 4 given that the number rolled is odd is 1/6.
Is 4 odd?
What is the probability of throwing an even number given the number thrown is odd?