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A bag contains only 3 different colours

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A bag contains only 3 different colours

by BTGmoderatorDC » Wed Nov 29, 2017 3:19 pm
A bag contains only 3 different colours and atleast one ball of red, white and blue colour. If the number of balls of each colour is distinct and red coloured balls are more than each of the other two colours, what is the probability of picking red ball?

(1) number of blue and white ball is half of total number of ball.
(2) there are 3 red coloured balls.

How will i find the correct statement?

OA D
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Nov 29, 2017 9:24 pm
lheiannie07 wrote:A bag contains only 3 different colours and atleast one ball of red, white and blue colour. If the number of balls of each colour is distinct and red coloured balls are more than each of the other two colours, what is the probability of picking red ball?

(1) number of blue and white ball is half of total number of ball.
(2) there are 3 red coloured balls.

How will i find the correct statement?

OA D
Say the number of red color balls = r; the number of white color balls = w; and the number of red color balls = b.

We know that either r > w > b or r > b > w

The probability of picking red ball = r/(r+w+b)

(1) The number of blue and white ball is half of the total number of balls.

We have w + b = (r+w+b)/2 => r = w+b

Thus, the probability of picking red ball = (w+b)/(w+b+w+b) = 1/2. Sufficient.

(2) There are 3 red colored balls.

Since there is at least one ball of each color and the number of balls is distinct, we have r = 3, w = 2 and b =1 OR r = 3, w = 1 and b = 2.

In either case, the probability of picking red ball = r/(r+w+b) = 3/(3+2+1) = 1/2. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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