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# A box contains only pens, pencils, and pads. If an item is randomly se

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Math Expert
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A box contains only pens, pencils, and pads. If an item is randomly se  [#permalink]

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16 Aug 2019, 01:47
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Difficulty:

35% (medium)

Question Stats:

55% (00:45) correct 45% (00:54) wrong based on 73 sessions

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A box contains only pens, pencils, and pads. If an item is randomly selected from the box, what is the probability that the item will be either a pencil or a pad?

(1) The probability that the item will be pad is 1/4.

(2) The probability that the item will be pen is 1/3.

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Re: A box contains only pens, pencils, and pads. If an item is randomly se  [#permalink]

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18 Aug 2019, 05:01
Let P(Pencil) be probability of finding a pencil. Similarly we will use P(Pen) and P(Pad) in our solution.
What we need to find is P ( either Pencil or Pad).
P(either Pencil or Pad) = P( not finding a Pen)

Statement 1
It does not help us find P(Pencil)
Not sufficient

Statement 2
P(Pen)=1/3
We have P (not finding a Pen) = 1 - P(Pen)= 1 - 1/3 = 2/3
SUfficient

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Re: A box contains only pens, pencils, and pads. If an item is randomly se  [#permalink]

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20 Aug 2019, 04:06
The event of selecting a pencil is mutually exclusive to the event of selecting a pad. Therefore, the probability of selecting a pencil or a pad will be the cumulative of the two probabilities.

From statement I, we know the probability of selecting a pad, but not for the pencil. Statement I is insufficient.
Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II we know that the probability of selecting a pen is $$\frac{1}{3}$$. Therefore, the cumulative probability of selecting a pencil or a pad = 1 – $$\frac{1}{3}$$ = $$\frac{2}{3}$$.
Statement II is sufficient. Answer options C and E can be eliminated.

The correct answer option is B.

Hope this helps!
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Re: A box contains only pens, pencils, and pads. If an item is randomly se  [#permalink]

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20 Aug 2019, 05:07
Bunuel wrote:
A box contains only pens, pencils, and pads. If an item is randomly selected from the box, what is the probability that the item will be either a pencil or a pad?

(1) The probability that the item will be pad is 1/4.

(2) The probability that the chip will be pen is 1/3.

chip should be replaced with item
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Re: A box contains only pens, pencils, and pads. If an item is randomly se  [#permalink]

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20 Aug 2019, 05:12
Bunuel wrote:
A box contains only pens, pencils, and pads. If an item is randomly selected from the box, what is the probability that the item will be either a pencil or a pad?

(1) The probability that the item will be pad is 1/4.

(2) The probability that the chip will be pen is 1/3.

Given: A box contains only pens, pencils, and pads.

Asked: If an item is randomly selected from the box, what is the probability that the item will be either a pencil or a pad?

(1) The probability that the item will be pad is 1/4.
Probability that the item will be pencil is unknown
NOT SUFFICIENT

(2) The probability that the item will be pen is 1/3.
A box contains only pens, pencils, and pads.
No of either pencil or a pad = Total - no of pens
the probability that the item will be either a pencil or a pad = 1 - The probability that the item will be pen is 1/3 = 2/3
SUFFICIENT

IMO B
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Math Expert
Joined: 02 Sep 2009
Posts: 58402
Re: A box contains only pens, pencils, and pads. If an item is randomly se  [#permalink]

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17 Sep 2019, 05:10
Bunuel wrote:
A box contains only pens, pencils, and pads. If an item is randomly selected from the box, what is the probability that the item will be either a pencil or a pad?

(1) The probability that the item will be pad is 1/4.

(2) The probability that the item will be pen is 1/3.

Official Explanation

We have an abundance of pens, pencils and pads. The probability that an item will be a pencil or a pad is (pencil or pen) = P(pencil) + P(pen), the sum of the individual probabilities, or else P(pencil or pen) = 1 - P(pen) , the probably that the item chosen is not a pen. On to the statements, separately first.

Statement (1) doesn't fit either case for sufficiency. The probability of a pencil could be 1/2, say, or 1/4, yielding different results to the question. Insufficient.

Statement (2) gives us sufficient information. The probability that the item is not a pen is 2/3, so the probability that the item is either a pencil or a pad is 2/3. Sufficient.

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Re: A box contains only pens, pencils, and pads. If an item is randomly se  [#permalink]

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17 Sep 2019, 05:10
Bunuel wrote:
A box contains only pens, pencils, and pads. If an item is randomly selected from the box, what is the probability that the item will be either a pencil or a pad?

(1) The probability that the item will be pad is 1/4.

(2) The probability that the item will be pen is 1/3.

Video Explanation

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Re: A box contains only pens, pencils, and pads. If an item is randomly se   [#permalink] 17 Sep 2019, 05:10
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