Events A and B are mutually exclusive.  Find the probability of A or B.  Express all the solution as a reduced fraction in the form a/b.

P(A) = 3/10

and P(B) = 1/4

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.

Learn how to calculate the probability of events A or B when they are mutually exclusive. Given probabilities P(A) = 3/10 and P(B) = 1/4, find the combined probability in reduced fraction form. Explore step-by-step solution and related questions.

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