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

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Carcass
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There are 12 pens and 5 pencils in box A. An object is picked at rando [#permalink] New post   31 Jan 2022, 06:14
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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] New post   31 Jan 2022, 06:24
Carcass wrote:
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. \(\frac{14}{17}\)

P(pen from box B) = P(pen from A AND pen from B OR pencil from A AND pen from B)
= P(pen from A AND pen from B) + P(pencil from A AND pen from B)
= [P(pen from A) x P(pen from B)] + [P(pencil from A) x P(pen from B)]
= [12/17 x 5/10] + [5/17 x 4/10]
= 60/170 + 20/170
= 80/170
= 8/17

Answer: A
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Re: There are 12 pens and 5 pencils in box A. An object is picked at rando [#permalink]
31 Jan 2022, 06:24
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