Problem Solving

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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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