A bag contains 4 red marbles and 5 marbles of other colors. A second

Question

A bag contains 4 red marbles and 5 marbles of other colors. A second bag contains 3 red marbles and 6 marbles of other colors. If 1 marble is selected at random from each bag, what is the probability that exactly 1 of the marbles will be red?

A. 4/27

B. 7/18

C. 13/27

D. 17/27

E. 55/81

Show Answer

Official Answer

C

A. 4/27

B. 7/18

C. 13/27

D. 17/27

E. 55/81

Pastillita · Answer

Is it (4C1*6C1 + 5C1*3C1) in the numerator and 9C1*9C1 in the denominator which gives 39/81 = 13/27 so C?

tanyatantan · Answer

I got D....? so where to check the answer?

Bunuel · Answer

The OA will be automatically revealed on Tuesday 12th of April 2022 08:45:03 AM Pacific Time Zone. At this time the OA will be available in the original post under the spoiler.

thkkrpratik · Answer

To get exactly 1 red marble, there are two scenarios that are favorable: 
1. Get 1 red marble from bag 1 AND get 0 red marbles from bag 2 
OR 
2. Get 0 red marbles from bag 1 AND get 1 red marble from bag 2

1. Get 1 red marble from bag 1 AND get 0 red marbles from bag 2 
= 4/9 (4 red marbles out of a total 9) x 6/9 (6 marbles of other colors out of a total 9) 
= 4/9 * 6/9
= 8/27

2. Get 0 red marbles from bag 1 AND get 1 red marble from bag 2
= 5/9 (5 marbles of other colors out of a total 9) x 3/9 (3 red marbles out of a total 9) 
= 5/9 * 3/9
= 5/27

As we need Case 1 OR Case 2, we add the probabilities

8/27 + 5/27 = 13/27

Option C

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A bag contains 4 red marbles and 5 marbles of other colors. A second

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