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A bag contains 6 red marbles and 4 white marbles.

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A bag contains 6 red marbles and 4 white marbles.

by BTGModeratorVI » Wed May 13, 2020 11:03 am

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A bag contains 6 red marbles and 4 white marbles. Alpha selects a marble from the bag at random, records its color and places it back in the bag. Then, Navarro selects a marble from the bag at random. What is the probability that Alpha and Navarro both select white marbles.

A. 4/25
B. 9/25
C. 2/5
D. 3/5
E. 4/5

Answer: A
Source: Princeton Review
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Re: A bag contains 6 red marbles and 4 white marbles.

by Jay@ManhattanReview » Thu May 14, 2020 10:47 pm
BTGModeratorVI wrote: ↑
Wed May 13, 2020 11:03 am
 A bag contains 6 red marbles and 4 white marbles. Alpha selects a marble from the bag at random, records its color and places it back in the bag. Then, Navarro selects a marble from the bag at random. What is the probability that Alpha and Navarro both select white marbles.

A. 4/25
B. 9/25
C. 2/5
D. 3/5
E. 4/5

Answer: A
Source: Princeton Review
For Alpha, the probability of drawing a white marble = 4/(4 + 6) = 4/10 = 2/5;

Since the drawn marble is replaced, we again have 6 red marbles and 4 white marbles in the bag.

Similarly, for Navarro, the probability of drawing a white marble = 4/(4 + 6) = 4/10 = 2/5;

Thus, the probability that Alpha and Navarro both select white marbles = 2/5*2/5 = 4/25

The correct answer: A

Hope this helps!

-Jay
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Re: A bag contains 6 red marbles and 4 white marbles.

by Brent@GMATPrepNow » Sat May 16, 2020 6:24 am
BTGModeratorVI wrote: ↑
Wed May 13, 2020 11:03 am
 A bag contains 6 red marbles and 4 white marbles. Alpha selects a marble from the bag at random, records its color and places it back in the bag. Then, Navarro selects a marble from the bag at random. What is the probability that Alpha and Navarro both select white marbles.

A. 4/25
B. 9/25
C. 2/5
D. 3/5
E. 4/5

Answer: A
Source: Princeton Review
P(both are white) = P(1st marble is white AND 2nd marble is white
= P(1st marble is white) x P(2nd marble is white)
= 4/10 x 4/10
= 16/100
= 4/25


Answer: A

Cheers,
Brent
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Re: A bag contains 6 red marbles and 4 white marbles.

by Scott@TargetTestPrep » Sat May 16, 2020 8:40 am
BTGModeratorVI wrote: ↑
Wed May 13, 2020 11:03 am
 A bag contains 6 red marbles and 4 white marbles. Alpha selects a marble from the bag at random, records its color and places it back in the bag. Then, Navarro selects a marble from the bag at random. What is the probability that Alpha and Navarro both select white marbles.

A. 4/25
B. 9/25
C. 2/5
D. 3/5
E. 4/5

Answer: A
Solution:

The probability that both select white marbles is 4/10 x 4/10 = 2/5 x 2/5 = 4/25.

Answer: A

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Re: A bag contains 6 red marbles and 4 white marbles.

by deloitte247 » Sun May 17, 2020 4:39 am
Total number of marbles = 10
Red marbles = 6
White marbles = 4

Probability of Alpha selecting a white marble = 4/10
Probability of Navarro selecting a white marble = 4/10

The probability that Alpha and Navarro both select white marbles =>
$$\frac{4}{10}\cdot\frac{4}{10}=\frac{2}{5}\cdot\frac{2}{5}=\frac{4}{25}$$

Answer =A
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