If a fair die is rolled, what is the probability of getting an even number, a number less than 5, a number larger than 6 and an odd number?
Even or Even = 3/6
Either-or probabilities are found by adding the individual probabilities.
<5 = P(1, 2, 3, or 4)
Die only has values 1-6.
To find the probability of multiple events occurring, you need to take into consideration that each event is independent and does not affect the probability of the other events.
Let's break down the question into separate events:
1. Getting an even number: There are three even numbers on a fair die (2, 4, and 6), so the probability of getting an even number is 3/6 or 1/2.
2. Getting a number less than 5: There are four numbers less than 5 on a fair die (1, 2, 3, and 4), so the probability of getting a number less than 5 is 4/6 or 2/3.
3. Getting a number larger than 6: Since a fair die only has numbers from 1 to 6, it is impossible to roll a number larger than 6. Therefore, the probability of getting a number larger than 6 is 0.
4. Getting an odd number: There are three odd numbers on a fair die (1, 3, and 5), so the probability of getting an odd number is 3/6 or 1/2.
To find the probability of all these events occurring together, you multiply the individual probabilities since the events are independent:
Probability = (1/2) * (2/3) * (0) * (1/2) = 0
Therefore, the probability of getting an even number, a number less than 5, a number larger than 6, and an odd number when rolling a fair die is 0. This means it is impossible for all these events to occur simultaneously.