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02 Jul 2021, 07:45
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
63% (02:47) correct
37%
(03:02)
wrong
based on 501
sessions
History
Date
Time
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Not Attempted Yet
Bag A contains 3 white and 3 red marbles. Bag B contains 6 white and 3 red marbles. One of the two bags will be chosen at random, and then two marbles will be drawn from that bag at random without replacement. What is the probability that the two marbles drawn will be the same color?
(A) 7/20
(B) 9/10
(C) 9/20
(D) 11/20
(E) 13/20
(A) 7/20
(B) 9/10
(C) 9/20
(D) 11/20
(E) 13/20
02 Jul 2021, 08:10
Kudos
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Probability of choosing a bag out of bag A and B= 1/2
Case 1: Bag A chosen
Subcase 1 : white balls are chosen -> 3/6 * 2/5
Subcase 2: red balls are chosen -> 3/6 * 2/5
subcase 1+ subcase 2 = 3/6 * 2/5 + 3/6 * 2/5 = 2 * (3/6 * 2/5 ) = 2/5
Case 2: Bag B chosen
Subcase 1 : white balls are chosen -> 6/9 * 5/8
Subcase 2: red balls are chosen -> 3/9 * 2/8
subcase 1+ subcase 2 = 6/9 * 5/8 + 3/9 * 2/8 = 1/2
Final probability = 1/2 (2/5 + 1/2) = 1/2 * (9/10) = 9/20
Correct Answer: C: 9/20
Case 1: Bag A chosen
Subcase 1 : white balls are chosen -> 3/6 * 2/5
Subcase 2: red balls are chosen -> 3/6 * 2/5
subcase 1+ subcase 2 = 3/6 * 2/5 + 3/6 * 2/5 = 2 * (3/6 * 2/5 ) = 2/5
Case 2: Bag B chosen
Subcase 1 : white balls are chosen -> 6/9 * 5/8
Subcase 2: red balls are chosen -> 3/9 * 2/8
subcase 1+ subcase 2 = 6/9 * 5/8 + 3/9 * 2/8 = 1/2
Final probability = 1/2 (2/5 + 1/2) = 1/2 * (9/10) = 9/20
Correct Answer: C: 9/20
General Discussion
04 Jul 2021, 04:48
Kudos
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Hi
can you please explain where is that 2/5 coming from??
can you please explain where is that 2/5 coming from??
