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# Box A contains 5 Red balls and 7 Green balls while box B contains

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e-GMAT Representative
Joined: 04 Jan 2015
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Box A contains 5 Red balls and 7 Green balls while box B contains  [#permalink]

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05 Mar 2019, 21:39
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Difficulty:

25% (medium)

Question Stats:

83% (02:08) correct 17% (02:07) wrong based on 18 sessions

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Box A contains 5 Red balls and 7 Green balls while box B contains 4 Red balls and 8 Green balls. From each of the boxes, 1 ball is randomly picked up. What is the probability that both the balls that were picked up are of the same colour?

A. $$\frac{19}{560}$$

B. $$\frac{19}{280}$$

C. $$\frac{1}{56}$$

D. $$\frac{1}{20}$$

E. $$\frac{19}{36}$$

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Joined: 17 Dec 2018
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Re: Box A contains 5 Red balls and 7 Green balls while box B contains  [#permalink]

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05 Mar 2019, 21:47
12 balls in each so there are 12×12= 144 possibilities

Outcomes where 2 reds drawn= 5 * 4 = 20

Outcomes where 2 green drawn= 8*7= 56

56+20= 76
76/144 = 19/36. IMO OA is E.

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Re: Box A contains 5 Red balls and 7 Green balls while box B contains  [#permalink]

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06 Mar 2019, 01:51
box 1 total balls = 12
and box 2 total balls = 12
so
red balls from both boxes = 5/12 * 4/12 = 20/144
and blue balls = 7/12 * 8/12 = 56/144

total P = 20+56/144 = 76/144
IMO E
$$\frac{19}{36}$$

EgmatQuantExpert wrote:
Box A contains 5 Red balls and 7 Green balls while box B contains 4 Red balls and 8 Green balls. From each of the boxes, 1 ball is randomly picked up. What is the probability that both the balls that were picked up are of the same colour?

A. $$\frac{19}{560}$$

B. $$\frac{19}{280}$$

C. $$\frac{1}{56}$$

D. $$\frac{1}{20}$$

E. $$\frac{19}{36}$$

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Joined: 11 Apr 2017
Posts: 20
Re: Box A contains 5 Red balls and 7 Green balls while box B contains  [#permalink]

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07 Mar 2019, 17:27
probability of picking 1 red ball from box A is 5/12
Probability of picking 1 red ball from box B is 4/12
Probability of picking 1 green ball from box A is 7/12
Probability of picking 1 green ball from box B is 8/12
Probability of picking ball of same colour is 5/12*4*12+7/12*8/12
=19/36
IMO-E
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2722
Re: Box A contains 5 Red balls and 7 Green balls while box B contains  [#permalink]

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07 Mar 2019, 22:24

Solution

Given:
In this question, we are given
• Box A contains 5 Red balls and 7 Green balls
• Box B contains 4 Red balls and 8 Green balls
• From each of the two boxes, 1 ball is randomly picked up

To find:
We need to determine
• The probability that both the balls that were picked up are of the same colour

Approach and Working:
We can have both balls of same colour in two possible ways:
• Both the balls are Red in colour
• Or, both the balls are Green in colour

The probability that both balls are Red = $$\frac{5}{12} * \frac{4}{12} = \frac{20}{144}$$
The probability that both balls are Green = $$\frac{7}{12} * \frac{8}{12} = \frac{56}{144}$$
• Therefore, the probability that both balls are of same colour = $$\frac{20}{144} + \frac{56}{144} = \frac{76}{144} = \frac{19}{36}$$

Hence, the correct answer is option E.

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Articles and Questions to reach Q51 | Question of the week | Tips From V40+ Scorers | V27 to V42:- GMAT 770 | Guide to Get into ISB-MBA

Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets

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Re: Box A contains 5 Red balls and 7 Green balls while box B contains   [#permalink] 07 Mar 2019, 22:24
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