If two events are independent, the probability of both events occurring is the product of their individual probability. Events A and B are independent with P(A)=0.3 and P(B)=0.25. What is the probability of events A and B happening at the same time? Write your answer in decimal form.(1 point)

Question

_

Answer 1

To find the probability of both events A and B occurring at the same time (their joint probability), we can use the formula for independent events:

\[ P(A \text{ and } B) = P(A) \times P(B) \]

Given that \( P(A) = 0.3 \) and \( P(B) = 0.25 \), we can substitute these values into the formula:

\[ P(A \text{ and } B) = 0.3 \times 0.25 \]

Calculating this gives:

\[ P(A \text{ and } B) = 0.075 \]

So, the probability of events A and B happening at the same time is \( \boxed{0.075} \).