Probability

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Probability

by swerve » Mon Jul 06, 2020 11:03 am

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Jenny's cabinet contains 4 bags of tortilla chips, 4 bags of potato chips, and 5 bags of popcorn. Jenny reaches into the cabinet and draws a bag at random, places it on the counter, and returns to draw one more bag at random. What is the probability that she pulls out two bags of popcorn?

A. 1/13
B. 5/39
C. 2/13
D. 3/13
E. 10/39

The OA is B

Source: Veritas Prep

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Source: Beat The GMAT — Problem Solving | Mon Jul 06, 2020 11:03 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

Re: Probability

by Jay@ManhattanReview » Mon Jul 06, 2020 11:20 pm

swerve wrote: ↑
Mon Jul 06, 2020 11:03 am
Jenny's cabinet contains 4 bags of tortilla chips, 4 bags of potato chips, and 5 bags of popcorn. Jenny reaches into the cabinet and draws a bag at random, places it on the counter, and returns to draw one more bag at random. What is the probability that she pulls out two bags of popcorn?

A. 1/13
B. 5/39
C. 2/13
D. 3/13
E. 10/39

The OA is B

Source: Veritas Prep

So, Jenney has a total of 13 bags; out of the 13, there are 5 bags of popcorn.

Probability of drawing the first bag being a popcorn bag = 5/13;
Probability of drawing the second bag being a popcorn bag = 4/12 = 1/3;

Thus, the probability of drawing both bags being popcorn bags = 5/13 * 1/3 = 5/39

Correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Probability

by Scott@TargetTestPrep » Sun Jul 12, 2020 2:30 pm

swerve wrote: ↑
Mon Jul 06, 2020 11:03 am
Jenny's cabinet contains 4 bags of tortilla chips, 4 bags of potato chips, and 5 bags of popcorn. Jenny reaches into the cabinet and draws a bag at random, places it on the counter, and returns to draw one more bag at random. What is the probability that she pulls out two bags of popcorn?

A. 1/13
B. 5/39
C. 2/13
D. 3/13
E. 10/39

The OA is B

Solution:

On the first draw, the probability of pulling a bag of popcorn is 5/13. Because Jenny doesn‘t put that bag back, there are now 12 bags in the drawer, 4 of which are popcorn, so the probability of popcorn on the second draw is 4/12.

Because we want to calculate the probability of both outcomes happening, we multiply their respective probabilities. Thus, the probability of pulling two bags of popcorn is:

5/13 x 4/12 = 5/13 x 1/3 = 5/39

Answer: B

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