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If two events are independent, the probability of both events occurring is the product of their individual probability. Events...Question
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)
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)
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Answered by
GPT-4o mini
To find the probability of both independent events A and B occurring at the same time, you multiply their individual probabilities together.
Given:
- \( P(A) = 0.3 \)
- \( P(B) = 0.25 \)
The probability of both A and B occurring, denoted as \( P(A \cap B) \), is calculated as follows:
\[
P(A \cap B) = P(A) \times P(B)
\]
Substituting the values:
\[
P(A \cap B) = 0.3 \times 0.25 = 0.075
\]
Therefore, the probability of events A and B happening at the same time is \( \boxed{0.075} \).
Given:
- \( P(A) = 0.3 \)
- \( P(B) = 0.25 \)
The probability of both A and B occurring, denoted as \( P(A \cap B) \), is calculated as follows:
\[
P(A \cap B) = P(A) \times P(B)
\]
Substituting the values:
\[
P(A \cap B) = 0.3 \times 0.25 = 0.075
\]
Therefore, the probability of events A and B happening at the same time is \( \boxed{0.075} \).
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