To find the probability of either event A or event B occurring when the events are mutually exclusive, we use the following formula:

$P(A \text{ or } B) = P(A) + P(B)$

Given: $P(A) = \frac{3}{10}$ $P(B) = \frac{1}{4}$

First, let's find a common denominator to add these fractions. The least common denominator (LCD) of 10 and 4 is 20.

Convert each probability to have a denominator of 20: $P(A) = \frac{3}{10} = \frac{3 \times 2}{10 \times 2} = \frac{6}{20}$ $P(B) = \frac{1}{4} = \frac{1 \times 5}{4 \times 5} = \frac{5}{20}$

Now, add the probabilities: $P(A \text{ or } B) = \frac{6}{20} + \frac{5}{20} = \frac{11}{20}$

Thus, the probability of A or B occurring is:

$\boxed{\frac{11}{20}}$

Would you like further details or have any questions?

Here are 5 related questions you might be interested in:

1. How do you calculate the probability of A or B if A and B are not mutually exclusive?
2. What happens to the probability of A or B if P(A) and P(B) overlap?
3. How would the answer change if P(A) was given as $\frac{1}{3}$?
4. Can you calculate the probability of neither A nor B occurring?
5. How does the formula for P(A and B) differ from P(A or B)?

Tip: When events are mutually exclusive, they cannot happen at the same time. This simplifies the calculation of their combined probability.