Probability

This topic has expert replies
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.

User avatar
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
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage