Probability

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Probability

by BTGmoderatorRO » Sat Nov 11, 2017 7:32 am

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.

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Source: Beat The GMAT — Problem Solving | Sat Nov 11, 2017 7:32 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

by EconomistGMATTutor » Sun Nov 12, 2017 9:50 am

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.

GMAT Prep From The Economist
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Sat Oct 26, 2019 7:37 am

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.

The probability that event B does not occur is 1 - 1/3 = 2/3.

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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