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# A box contains 7 red marbles, 5 blue marbles and 8 green mar

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A box contains 7 red marbles, 5 blue marbles and 8 green mar [#permalink]  20 Jun 2017, 11:16
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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
[Reveal] Spoiler: OA

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Last edited by pranab01 on 28 Jun 2017, 19:11, edited 2 times in total.
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Re: A box contains 7 red marbles, 5 blue marbles and 8 green mar [#permalink]  28 Jun 2017, 06:34
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Probability of picking 2 red marbles = (7/20)*(6/19)
Probability of picking 2 blue marbles = (5/20)*(4/19)
Probability of picking 2 green marbles = (8/20)*(7/19)

As the above 3 events are mutually exclusive,
Probability of picking matching marbles = Probability of picking 2 red marbles + Probability of picking 2 blue marbles + Probability of picking 2 green marbles
= (7/20)*(6/19) + (5/20)*(4/19) + (8/20)*(7/19)
= 59/190

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Re: A box contains 7 red marbles, 5 blue marbles and 8 green mar [#permalink]  26 Jul 2017, 01:01
nainy05 wrote:
Probability of picking 2 red marbles = (7/20)*(6/19)
Probability of picking 2 blue marbles = (5/20)*(4/19)
Probability of picking 2 green marbles = (8/20)*(7/19)

As the above 3 events are mutually exclusive,
Probability of picking matching marbles = Probability of picking 2 red marbles + Probability of picking 2 blue marbles + Probability of picking 2 green marbles
= (7/20)*(6/19) + (5/20)*(4/19) + (8/20)*(7/19)
= 59/190

Hi! I have a question here - why do we consider the denominator of the total base (7+5+8 =20) to be 19? I understand why take 7/20 (total probability. Would require a little more explanation here, thank you!
Director
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Re: A box contains 7 red marbles, 5 blue marbles and 8 green mar [#permalink]  26 Jul 2017, 03:30
nancyjose wrote:
nainy05 wrote:
Probability of picking 2 red marbles = (7/20)*(6/19)
Probability of picking 2 blue marbles = (5/20)*(4/19)
Probability of picking 2 green marbles = (8/20)*(7/19)

As the above 3 events are mutually exclusive,
Probability of picking matching marbles = Probability of picking 2 red marbles + Probability of picking 2 blue marbles + Probability of picking 2 green marbles
= (7/20)*(6/19) + (5/20)*(4/19) + (8/20)*(7/19)
= 59/190

Hi! I have a question here - why do we consider the denominator of the total base (7+5+8 =20) to be 19? I understand why take 7/20 (total probability. Would require a little more explanation here, thank you!

Here total no. of marbles is 20 only on first selection, but in the next selection we are left with only 19 marbles instead of 20 so denominator becomes 19. However if we need to take out one more than the denominator will become 18.

Since probability = $$\frac{favorable outcome}{total number of outcomes}$$

Hope it clears
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Re: A box contains 7 red marbles, 5 blue marbles and 8 green mar [#permalink]  04 May 2018, 09:29
Expert's post
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.

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Re: A box contains 7 red marbles, 5 blue marbles and 8 green mar   [#permalink] 04 May 2018, 09:29
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# A box contains 7 red marbles, 5 blue marbles and 8 green mar

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