A box contains only red chips, white chips, and blue chips.

Question

A box contains only red chips, white chips, and blue chips. If a chip is randomly selected from the box, what is the probability that the chip will be either white or blue?

(1) The probability that the chip will be blue is 1/5.
(2) The probability that the chip will be red is 1/3.

Bunuel · Accepted Answer

A box contains only red chips, white chips, and blue chips. If a chip is randomly selected from the box, what is the probability that the chip will be either white or blue?

The probability that the chip will be either white or blue, equals to the probability that the chip will NOT be red, thus P(white or blue)=1-P(red).

(1) The probability that the chip will be blue is 1/5. Not sufficient.

(2) The probability that the chip will be red is 1/3. P(white or blue)=1-P(red)=1-1/3=2/3. Sufficient.

Answer: B.

KarishmaB · Answer

The concept of mutually exclusive and exhaustive events helps us understand which methodology to use in which question.
Two events are mutually exclusive when they cannot both happen at the same time. e.g. picking a white chip and picking a blue chip are mutually exclusive events. If you pick out one chip, it will be either white or blue but not both.

When 2 or more events represent all possible events, they are called exhaustive events. Picking a white chip, picking a blue chip and picking a red chip are mutually exclusive and exhaustive events. When you pick out a chip, it has to be either blue or white or red. It cannot be a fourth color. Hence these 3 events represent all possible events that can take place. The sum of their probabilities will be 1. This is so because one of them HAS to take place.

In this question, when we know that probability of a red chip is 1/3, what is the remaining 2/3 probability? It is the probability that we will get either a white chip or a blue chip. Hence statement 2 is sufficient.

On the other hand, statement 1 just gives you the probability of blue chip as 1/5. This means 1/5th of the chips are blue but you do not know the probability of getting a white chip. So you do not know the probability of getting a white or a blue chip. If we had both P(blue) and P(white), we would have calculated it as:
P(blue or white) = P(blue) + P(white)

ClariceM · Answer

For those wondering, you could also find this answer another way. The way presented above is the fastest, but, just in case you are wondering, like I was, you could also do the following:

find the value of P(white) by doing:

1 - ( P(B) + P(R) ) = P(W)

Then do:

P(W or B) = P(W) + P(B) - P( W and B)

here P (W and B) is equal to zero, because it is not independent, it is mutually exclusive. (it is mutually exclusive because if you get one red you cannot get one white for example).

so it is simply:

P(W or B) = P(W) + P(B) - 0

Here is the calculation with numbers:

1- ( 1/5 + 1/3) = 7/15 = P(W)

now do: P(W or B) = P(W) + P(B) - 0

7/15 + 1/5 - 0 = 2/3

hope it helps!
I was wondering about this other method when I did the problem.

hope it helps! I was wondering about this other method when I did the problem.

faizanqazi · Answer

concept :

For second .

P(R) + P (B) + P (W) = 1

P (W) + P(B) = 1 - P(R)

P(R) IS GIVEN.
so 2 is sufficient.

BrentGMATPrepNow · Answer

Target question :    What is the probability that the chip is either white or blue?

Given : The box contains only red chips, white chips, and blue chips

Statement 1 : The probability that the chip will be blue is 1/5. 
This tells us that 1/5 of the chips are BLUE, but there's no information about the WHITE chips.

Consider these two possible cases: 
 Case a : There are 5 chips in total. 1 chip is blue, and 1 chip is white. In this case, the answer to the target question is  P(chip is either white or blue) = 2/5 
 Case b : There are 5 chips in total. 1 chip is blue, and 2 chips are white. In this case, the answer to the target question is  P(chip is either white or blue) = 3/5 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : The probability that the chip will be red is 1/3  
This also tells us that  the probability of selecting a NON-RED chip is 2/3 
Since the box contains only red chips, white chips, and blue chips, then selecting a NON-RED chip is the same as selecting either a BLUE chip OR a WHITE chip
In other other words, P(select NON-BLUE chip) = P(selecting either a BLUE chip OR a WHITE chip)
So, the answer to the target question is  P(chip is either white or blue) = 2/3

Answer: B

Cheers,
Brent

GMATCoachBen · Answer

https://www.youtube.com/watch?v=FrvUlXjea7U

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A box contains only red chips, white chips, and blue chips.

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