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# Colleen times her morning commute such that there is an equal likeliho

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Intern
Joined: 21 Jun 2014
Posts: 30
Colleen times her morning commute such that there is an equal likeliho  [#permalink]

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Updated on: 26 May 2015, 04:33
16
00:00

Difficulty:

85% (hard)

Question Stats:

43% (01:55) correct 57% (02:14) wrong based on 141 sessions

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Colleen times her morning commute such that there is an equal likelihood that she will arrive early or late to work on any given day. If she always arrives either early or late, what is the probability that Colleen will arrive late to work no more than twice during a five-day workweek?

(A) 1/4
(B) 15/32
(C) 1/2
(D) 1732
(E) 3/4

HTTTT + HHTTT
= 5c1/32 + 5c2/32 = 15/32 (But not correct answer)

Originally posted by sandeepmanocha on 25 May 2015, 12:44.
Last edited by Bunuel on 26 May 2015, 04:33, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1323
Re: Colleen times her morning commute such that there is an equal likeliho  [#permalink]

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25 May 2015, 14:04
2
sandeepmanocha wrote:
HTTTT + HHTTT
= 5c1/32 + 5c2/32 = 15/32 (But not correct answer)

Your thinking is right here, but you missed one case. If you think of it as a coinflip problem, it is also possible that all 5 flips are tails: TTTTT. Since that has a (1/2)^5 = 1/32 chance of happening, that's the reason your answer was too low by exactly 1/32.

There's a slightly faster way to do the problem. The probability she will be late at most 2 times is exactly the same as the probability she will be early at most 2 times. But those are all the possible scenarios, so each must happen 1/2 the time.
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Intern
Joined: 21 Jun 2014
Posts: 30
Re: Colleen times her morning commute such that there is an equal likeliho  [#permalink]

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25 May 2015, 14:54
IanStewart wrote:
Your thinking is right here, but you missed one case. If you think of it as a coinflip problem, it is also possible that all 5 flips are tails: TTTTT. Since that has a (1/2)^5 = 1/32 chance of happening, that's the reason your answer was too low by exactly 1/32.

Thanks for pointing, and yes AT MOST means, 0 or more upto given limit. It is going into my Tips

IanStewart wrote:
There's a slightly faster way to do the problem. The probability she will be late at most 2 times is exactly the same as the probability she will be early at most 2 times. But those are all the possible scenarios, so each must happen 1/2 the time.

Thanks
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Posts: 1323
Re: Colleen times her morning commute such that there is an equal likeliho  [#permalink]

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25 May 2015, 17:23
2
1
Say you flip a coin 5 times, and are asked two questions:

1. what's the probability you get more Heads than Tails?
2. what's the probability you get more Tails than Heads?

the answer to those two questions must be the same, because, since it's equally likely you get Heads or Tails on each toss, there's no logical reason why the answer to question 1 should be lower or higher than the answer to question 2.

But the situations in 1 and 2 are the only things that can possibly happen - we can't get an equal number of H and T if we flip a coin an odd number of times. And the probabilities of all the things that can happen must add up to 1. So we have two equal probabilities that add to 1, and both probabilities must be 1/2.

Notice that question 2, "what's the probability you get more Tails than Heads" is exactly the question you were answering: it's the same question as: "what's the probability you get at most 2 Heads if you flip a coin 5 times?"

So that's one way to see that the answer is 1/2 here without looking at any cases.
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Manager
Joined: 29 May 2016
Posts: 101
Re: Colleen times her morning commute such that there is an equal likeliho  [#permalink]

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10 Sep 2016, 04:17
probability that Colleen will arrive late to work no more than twice
what does that mean, shall i consider at-least one till max 2 than answer will be 15/32

but if we can consider even a zero case of late than answer will be be C 16/32= 1/2

Intern
Joined: 26 Jan 2014
Posts: 7
Re: Colleen times her morning commute such that there is an equal likeliho  [#permalink]

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21 May 2017, 15:16
mbaprep2016 wrote:
probability that Colleen will arrive late to work no more than twice
what does that mean, shall i consider at-least one till max 2 than answer will be 15/32

but if we can consider even a zero case of late than answer will be be C 16/32= 1/2

Yes, you are right. At most 2 includes "not late even once" so the answer would be 15/32 + 1/32 = 1/2.
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Posts: 331
Re: Colleen times her morning commute such that there is an equal likeliho  [#permalink]

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22 May 2017, 11:34
1
1
Case 1: Colleen was late on 0 out of 5 days.

==> 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32

Case 2: Colleen was late on 1 out of 5 days.

==> 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 5C1

==> 1/32 * 5 = 5/32

Case 3: Colleen was late on 2 out of 5 days.

==> 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 5C2

==> 1/32 * 10 = 5/16

Probability that Colleen will arrive late to work no more than twice during a five-day workweek

= 1/32 + 5/32 + 5/16 = 16/32 = 1/2

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Re: Colleen times her morning commute such that there is an equal likeliho  [#permalink]

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22 Sep 2018, 13:24
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Re: Colleen times her morning commute such that there is an equal likeliho &nbs [#permalink] 22 Sep 2018, 13:24
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