A box contains 7 red marbles, 5 blue marbles and 8 green marbles. John

Question

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

EgmatQuantExpert · Answer

Solution

Given:  
• A bag contains 7 red, 5 blue, and 8 green marbles
 o Total number of marbles = 20 
• John picks up 2 marbles at random from the box

To find:  
• The probability that John has picked a pair of matching marbles

Approach and Working:   
• The number of ways John can pick 2 marbles at random =  ^{20}C_2  = 190 ways
• If he picks 2 marbles of same color, then he can pick
 o 2 red marbles in  ^7C_2  = 21 ways 
 o 2 blue marbles in  ^5C_2  = 10 ways 
 o 2 green marbles in  ^8C_2  = 28 ways 
• Therefore, the probability of picking a pair of matching marbles =  \frac{(21 + 10 + 28)}{190} = \frac{59}{190}

Hence, the correct answer is option D.

Answer: D

Tulkin987 · Answer

\frac{7}{20}*\frac{6}{19} + \frac{5}{20}*\frac{4}{19} + \frac{8}{20}*\frac{7}{19}   = \frac{1}{19*20}(42+20+56) = \frac{118}{19*20} = \frac{59}{190}

Answer: D

BrentGMATPrepNow · Answer

P(matching marbles) = P(both are red    OR    both are blue    OR    both are green)
= P(red 1st  and  red 2nd    OR    blue 1st  and  blue 2nd    OR    green 1st  and  green 2nd)
= P(red 1st  and  red 2nd)    +    P(blue 1st  and  blue 2nd)    +    P(green 1st  and  green 2nd)
=  x  P(red 2nd)]    +     x  P(blue 2nd)]    +     x  P(green 2nd)]
=  x  6/19]    +     x  4/19]    +     x  7/19]
= 42/380    +    20/380    +    56/380
= 118/380
= 59/190

Answer: D

JeffTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

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.

Total no of ways to select 2 marbles from 20 marbles ( 7 R + 5B + 8G) = 20C2 = 190

No ways to select pair of matching marbles = Select 2 marbles from 7 red or Select 2 marbles from 5 blue or Select 2 marbles from 8 green= 7C2 + 5C2 + 8C2 = 21 + 10 + 28 = 59

Therefore, P( picked a pair of matching marbles) = Favorable outcomes / Total outcomes = 59/190

Option D is the answer.

Thanks,
Clifin J Francis.

flippedeclipse · Answer

Probability is  \frac{favourable outcomes}{all outcomes}

All outcomes:  C^{20}_2=\frac{20*19}{2}=190

Favourable outcomes are picking 2 of the same marble, but each double-pick exists in a separate "universe" from each other, so we add them.

C^7_2+C^5_2+C^8_2=\frac{7*3}{2}+\frac{5*4}{2}+\frac{8*7}{2}=59

Thus probability is  \frac{59}{190} .

A box contains 7 red marbles, 5 blue marbles and 8 green marbles. John

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