The probability that an event A occurs is 1/2 and the probability that an even B occurs is 1/3. If event A and event B are independent, what is the probability that event A occurs but event B does not occur?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6
OA is b
Can someone expatiate on why B is the correct answer. Thanks for your time.
Probability
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Hello Roland2rule.
As the probability that event B occurs is 1/3, then the probability that event B doesn't occur is 2/3.
In the question " what is the probability that event A occurs but event B does not occur?", it is asked for both events at the same time. So, the probability of this is $$P\left(A\right)\cdot P\left(No\ B\right)=\frac{1}{2}\cdot\frac{2}{3}=\frac{1}{3}.$$
So, the correct answer is B .
I'm available if you'd like a follow up.
Regards.
As the probability that event B occurs is 1/3, then the probability that event B doesn't occur is 2/3.
In the question " what is the probability that event A occurs but event B does not occur?", it is asked for both events at the same time. So, the probability of this is $$P\left(A\right)\cdot P\left(No\ B\right)=\frac{1}{2}\cdot\frac{2}{3}=\frac{1}{3}.$$
So, the correct answer is B .
I'm available if you'd like a follow up.
Regards.
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The probability that event B does not occur is 1 - 1/3 = 2/3.BTGmoderatorRO wrote:The probability that an event A occurs is 1/2 and the probability that an even B occurs is 1/3. If event A and event B are independent, what is the probability that event A occurs but event B does not occur?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
E. 5/6
OA is b
Can someone expatiate on why B is the correct answer. Thanks for your time.
We want the probability that A occurs AND that B does not occur. Because events A and B are independent, we can multiply the respective probabilities. Thus, the probability that event A occurs but event B does not occur is 1/2 x 2/3 = 1/3.
Answer: B
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