Find the probability of getting either a number multiple of 3 or a prime number when a fair die is thrown

Sure, let's break this down:

1. Identify the total number of outcomes: When a fair die is thrown, there are 6 possible outcomes (1, 2, 3, 4, 5, 6).

2. Identify the favorable outcomes for getting a number multiple of 3: The multiples of 3 in this range are 3 and 6. So, there are 2 favorable outcomes.

3. Identify the favorable outcomes for getting a prime number: The prime numbers in this range are 2, 3, and 5. So, there are 3 favorable outcomes.

4. Combine the favorable outcomes: However, the number 3 is both a multiple of 3 and a prime number, so it gets counted twice. To avoid this, we use the principle of Inclusion and Exclusion. We add the number of multiples of 3 and the number of primes, then subtract the overlap. So, there are 2 + 3 - 1 = 4 favorable outcomes.

5. Calculate the probability: The probability of an event is the number of favorable outcomes divided by the total number of outcomes. So, the probability of getting either a multiple of 3 or a prime number is 4/6 = 2/3.