Two events A and B have probabilities 0.25 and 0.5 respectively. The probabilities that A and B occur simultaneously is 0.15. Then the probability that A or B occurs is

Options

A. 0.61
B. `0.7`
C. `0.61`
D. `0.72`

Answer

To find the probability that either event A or event B occurs, we can use the formula for the probability of the union of two events. The formula is:

\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]

Where:
- \(P(A \cup B)\) is the probability that either A or B occurs.
- \(P(A)\) is the probability of event A occurring.
- \(P(B)\) is the probability of event B occurring.
- \(P(A \cap B)\) is the probability that both events A and B occur simultaneously.

**Step 1: Identify the given probabilities.**
- \(P(A) = 0.25\)
- \(P(B) = 0.5\)
- \(P(A \cap B) = 0.15\)

**Step 2: Substitute the values into the formula.**
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \]
\[ P(A \cup B) = 0.25 + 0.5 - 0.15 \]

**Step 3: Perform the addition and subtraction.**
\[ P(A \cup B) = 0.75 - 0.15 \]
\[ P(A \cup B) = 0.60 \]

**Step 4: Write the final answer.**
The probability that either event A or event B occurs is \(0.60\).

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