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There are 12 pens and 5 pencils in box A. An object is picked at rando

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There are 12 pens and 5 pencils in box A. An object is picked at rando  [#permalink]

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New post 06 Apr 2019, 22:01
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A
B
C
D
E

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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Re: There are 12 pens and 5 pencils in box A. An object is picked at rando  [#permalink]

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New post 06 Apr 2019, 22:53
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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
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Re: There are 12 pens and 5 pencils in box A. An object is picked at rando  [#permalink]

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New post 07 Apr 2019, 12:31
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
therefore addition : answer = 6/17+2/17= 8/17
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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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