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SC Moderator V
Joined: 23 Sep 2015
Posts: 1713
There are 12 pens and 5 pencils in box A. An object is picked at rando  [#permalink]

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2 00:00

Difficulty:   35% (medium)

Question Stats: 68% (02:03) correct 32% (02:20) wrong based on 30 sessions

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There are 12 pens and 5 pencils in box A. An object is picked at random from box A and moved to box B, in which there are already 4 pens and 5 pencils. If one object is then to be picked from box B, what is the probability that a pen will be picked?

A. $$\frac{8}{17}$$

B. $$\frac{80}{153}$$

C. $$\frac{9}{17}$$

D. $$\frac{12}{17}$$

E. $$\frac{14}{17}$$

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Intern  S
Joined: 22 Apr 2018
Posts: 32
Re: There are 12 pens and 5 pencils in box A. An object is picked at rando  [#permalink]

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3
Here is my take:
When calculating the probability of multiple events that must ALL occur to meet a certain condition, we Must MULTIPLY the separate possibilities off each event together:
Now, Probability of Selecting a Pen from the both the boxes A and B will be:
12/17(from box A) * 5/10(from box B) = 60/170

Again, Probability of Selecting a Pencil from the box A and selecting a pen from box B will be:
5/17 * 4/10 = 20/170

When calculating the probability of a series of Mutually Exclusive events where ANY event occurring would be sufficient, we must add the separate possibilities of each event together
thus Probability a Pen will be picked will be: 60/170+20/170 = 80/170 = 8/17
Senior Manager  G
Joined: 04 Apr 2015
Posts: 254
GMAT 1: 650 Q49 V31 GPA: 3.59
Re: There are 12 pens and 5 pencils in box A. An object is picked at rando  [#permalink]

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we know we have to transfer 1 thing from box A to BOX B and then again choose from box B

Case 1 '
we choose a pen (so probability of choosing pen from A and then probability of choosing pen from Box B ,which has now 5 pen 5 pencils)
12/17 * 5/10 = 6/17

Case 2:
we choose a pencil in first case (so probab. of choosing pencil From A and then prob. choosing pen from box B ,which has no 4 pen and 6 pencil)
5/17*4/10= 2/17

only one of the case will happen so AN OR operator Re: There are 12 pens and 5 pencils in box A. An object is picked at rando   [#permalink] 07 Apr 2019, 12:31
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