Question

P(A) = 0.60 and P(B) =0.20, and P(A or B)=0.15. What is P(A or B)?

Answer 1

The probability of either event A or event B occurring (P(A or B)) is 0.65, calculated using the inclusion-exclusion principle with given probabilities: P(A) = 0.60, P(B) = 0.20, and P(A or B) = 0.15.

The probability of either event A or event B occurring, denoted as P(A or B), can be calculated using the inclusion-exclusion principle:

`\[ P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) \]`

Given that
`\( P(A) = 0.60 \), \( P(B) = 0.20 \)`, and
`\( P(A \text{ or } B) = 0.15 \)`, we can plug these values into the formula:

`\[ 0.15 = 0.60 + 0.20 - P(A \text{ and } B) \]`

Now, solve for
`\( P(A \text{ and } B) \)`:

`\[ P(A \text{ and } B) = 0.60 + 0.20 - 0.15 \]\[ P(A \text{ and } B) = 0.65 \]`

Therefore, the probability of both events A and B occurring is
`\( P(A \text{ and } B) = 0.65 \)`.