pranab01 wrote:
A box contains 7 red marbles, 5 blue marbles and 8 green marbles. John picks up two marbles at a random from the the bag. What is the probability that John has picked a pair of matching marbles
(A) 1/19
(B) 15/90
(C) 7/19
(D) 59/190
(E) 2/190
We have 3 possible scenarios: 1) 2 reds, 2) 2 blues, and 3) 2 greens, thus:
Number of ways to select 2 reds is 7C2 = 7!/(2! x 5!) = (7 x 6)/2 = 21.
Number of ways to select 2 blues is 5C2 = 5!/(2! x 3!) = (5 x 4)/2! = 10.
Number of ways to select 2 greens is 8C2 = 8!/(2! x 6!) = (8 x 7)/2! = 28.
Number of ways to select any 2 marbles from 20 is 20C2 = 20!/(2! x 18!) = (20 x 19)/2 = 190.
Therefore, P(picking a pair of same-color marbles) = (21 + 10 + 28)/190 = 59/190.
Answer: D
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