Data Sufficiency

AAPL wrote:Mike's pencil box contains 30 pens. 15 of the pens are red, and all of the others are either blue or black. If Mike were to choose a random pen from the pencil box, what is the probability that it would be blue?

1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3
2) The probability that the pen will be red or blue is 0.8

The OA is D.

Could anyone help me calculating the probabilities of picking a blue pencil? DS is clear for me, but I'm not sure about the true calculation of the numbers.

Since there are 15 (= 1/2 of 30) numbers of Red pens, the probability that it would be Red = 15/30 = 0.5. Say P(R) = 0.5.

We have to find out the probability that the pen from the pencil box would be blue. Say it is P(Bl). And say the probability that the pen from the pencil box would be black = P(Bk)

Let's take each statement one by one.

1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3.

P(R) - P(Bk) = 0.3

=> P(Bk) = 0.5 - 0.3 = 0.2

We know that P(R) + P(Bk) + P(Bl) = 1

Thus, P(Bl) = 1 - P(R) - P(Bk)

P(Bl) = 1 - 0.5 - 0.2

P(Bl) = 0.3. Sufficient.

2) The probability that the pen will be red or blue is 0.8.

=> P(R) + P(Bl) = 0.8

P(Bl) = 0.8 - P(R) = 0.8 - 0.5 = 0.3. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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Hi All,

We're told that Mike's pencil box contains 30 pens, 15 of the pens are red, and all of the others are either blue OR black. We're asked if Mike were to choose a random pen from the pencil box, what is the probability that it would be BLUE. This question can be approached in a couple of different ways - either by focusing on the probabilities or on the number of each type of pen.

1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3

We know that there are 15 red pens, so the probability of pulling a red pen is 15/30 = 1/2 = .5
With the information in Fact 1, we know that the DIFFERENCE between the probability of pulling a red and the probability of pulling a black is .3, so....
.5 - .3 = .2
The probability of pulling a black pen is .2, so there are (30)(.2) = 6 black pens
With a total of 30 pens.... 15 red and 6 black... leaves us with 30 - 15 - 6 = 9 blue pens and the probability of pulling a blue pen is 9/30 = .3
Fact 1 is SUFFICIENT

2) The probability that the pen will be red or blue is 0.8

With the information in Fact 2, we can take the same general approach that we used in Fact 1:

We know that there are 15 red pens, so the probability of pulling a red pen is 15/30 = 1/2 = .5
With the information in Fact 2, we know that the total probability of pulling a red or blue pen is .8, so....
.5 + .3 = .8
Thus, the probability of pulling a blue pen is .3
Fact 2 is SUFFICIENT

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:Mike's pencil box contains 30 pens. 15 of the pens are red, and all of the others are either blue or black. If Mike were to choose a random pen from the pencil box, what is the probability that it would be blue?

1) The probability that the pen will be red minus the probability that the pen will be black equals 0.3
2) The probability that the pen will be red or blue is 0.8

We see that the P(red) = 15/30 = 0.5 and thus P(blue or black) = P(blue) + P(black) = 0.5. We need to determine P(blue). So if we know P(black), then we can determine P(blue) since P(blue) = 0.5 - P(black).

Statement One Alone:

The probability that the pen will be red minus the probability that the pen will be black equals 0.3.

So we have:

P(red) - P(black) = 0.3

0.5 - P(black) = 0.3

P(black) = 0.2

Thus, P(blue) = 0.5 - 0.2 = 0.3. Statement one alone is sufficient.

Statement Two Alone:

The probability that the pen will be red or blue is 0.8.

So we have:

P(red) + P(blue) = 0.8

0.5 + P(blue) = 0.8

P(blue) = 0.3

Statement two alone is also sufficient.

Answer: D