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02 Dec 2024, 07:32
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
75% (02:21) correct
25%
(02:06)
wrong
based on 205
sessions
History
Date
Time
Result
Not Attempted Yet
There are 5 red balls, 6 blue balls and 3 green balls in a box. If two balls are picked without replacement from the box, what is the probability that they are of different colours?
(A) 9/26
(B) 8/13
(C) 9/14
(D) 9/13
(E) 4/7
(A) 9/26
(B) 8/13
(C) 9/14
(D) 9/13
(E) 4/7
02 Dec 2024, 08:40
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R=5
B=6
G=3
Total= 5+6+3=14
Balls are diff Colors= (B,R)+(B,G)+(R,G)+(G,R) + (R,B)+(G,B)+(R,G)
= (6/14)*(5/13)+(6/14)*(3/13)+(5/14)*(3/13)+(5/14)*(6/13)+(3/14)*6/13)+(3/14)*(5/13)
= 2* [(30/182)+(18/182)+(15/182)]
= 2*(63/182)
= 63/91
= 9/13
Answer: D
B=6
G=3
Total= 5+6+3=14
Balls are diff Colors= (B,R)+(B,G)+(R,G)+(G,R) + (R,B)+(G,B)+(R,G)
= (6/14)*(5/13)+(6/14)*(3/13)+(5/14)*(3/13)+(5/14)*(6/13)+(3/14)*6/13)+(3/14)*(5/13)
= 2* [(30/182)+(18/182)+(15/182)]
= 2*(63/182)
= 63/91
= 9/13
Answer: D
07 Dec 2024, 09:45
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navigator01
As they didn't mention any thing about the size of balls, We can consider all are different.
So selecting 2 balls out of the 14 balls . \(14C2\) = 91.
Favorable outcomes R,B = 30
B,G = 6*3 = 18
R,G = 5*3 = 15
Total favorable outcomes = 63.
Probability = 63/91 =>9/13
IMO D
