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

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Manager
Joined: 02 Dec 2012
Posts: 177
A box contains only red chips, white chips, and blue chips.  [#permalink]

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14 Dec 2012, 04:19
2
18
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:47) correct 30% (01:00) wrong based on 1102 sessions

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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.
Math Expert
Joined: 02 Sep 2009
Posts: 51285
Re: A box contains only red chips, white chips, and blue chips.  [#permalink]

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14 Dec 2012, 04:23
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.

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Re: A box contains only red chips, white chips, and blue chips.  [#permalink]

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14 Dec 2012, 04:35
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.

Too simple

To find : probability of white or blue (which is equivalent to 1-probability of red)

S1 : there is no probability of white -- INSUFF
S2 : red - 1/3
Therefore p(W/B) = $$1-1/3 = 2/3$$
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Intern
Joined: 14 Apr 2017
Posts: 1
Re: A box contains only red chips, white chips, and blue chips.  [#permalink]

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14 May 2017, 00:54
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!
Intern
Joined: 09 Jan 2017
Posts: 6
Re: A box contains only red chips, white chips, and blue chips.  [#permalink]

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25 Jul 2017, 05:46
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.
CEO
Joined: 11 Sep 2015
Posts: 3243
Re: A box contains only red chips, white chips, and blue chips.  [#permalink]

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12 Aug 2018, 05:10
Top Contributor
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.

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

Cheers,
Brent
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Re: A box contains only red chips, white chips, and blue chips. &nbs [#permalink] 12 Aug 2018, 05:10
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