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## OG On Saturday morning, Malachi will begin camping

tagged by: Brent@GMATPrepNow

This topic has 5 expert replies and 0 member replies
AbeNeedsAnswers Master | Next Rank: 500 Posts
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#### OG On Saturday morning, Malachi will begin camping

Thu Jul 27, 2017 9:22 pm
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

B

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Jay@ManhattanReview GMAT Instructor
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Thu Jul 27, 2017 9:28 pm
AbeNeedsAnswers wrote:
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

B
Hi AbeNeedsAnswers,

I see that you have been posting many questions. Many questions have already been answered by the experts. Suggest you to first search the question before posting them.

Pl. see the solution here.

http://www.beatthegmat.com/og-on-saturday-morning-malachi-will-begin-a-t293431.html

Hope this helps!

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-Jay
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Brent@GMATPrepNow GMAT Instructor
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Fri Jul 28, 2017 5:19 am
AbeNeedsAnswers wrote:
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

B
NOTE: if P(rain on a certain day) = 0.2, then we know that P(NO rain on a certain day) = 1 - 0.2 = 0.8

For probability questions, I always ask, "What needs to happen for the desired event to occur?"

For this question P(come home Monday night) = P(no rain on Saturday AND no rain on Sunday AND rain on Monday)

At this point, we can apply what we know about AND probabilities. We get:
P(come home Monday night) = P(no rain on Saturday) X P(no rain on Sunday) X P(rain on Monday)
= (0.8) X (0.8) X (0.2)
= 0.128
= B

Cheers,
Brent

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Sat Jul 29, 2017 10:04 am
Hi AbeNeedsAnswers,

The standard approach to these types of probability questions is to determine the probability of each individual 'event', then multiply those probabilities together. With this question, there's a minor Number Property 'shortcut' at the end that can save you some time (and it helps if you're paying attention to how the answers are 'spaced out.'

Here, we're told:
-the probability of rain occurring on any individual day = 0.2
-thus, the probability of rain NOT occurring on any individual day = 1 - 0.2 = 0.8

For Malachi to return at the end of the day on Monday, the following series of events must occur:
(No rain on Saturday)(No rain on Sunday)(Rain on Monday).

The probability of that exact chain of events is:
(.8)(.8)(.2)

At this point, you could just multiply those numbers together, but here's that math shortcut I referred to earlier: multiplying any positive number by a positive fraction (between 0 and 1) will result in a SMALLER number. Since we're multiplying 3 positive fractions together, the result WILL be less than 0.2.... Thus, the correct answer MUST be either A or B.

You probably already know that 2x2x2 = 8. IF.... you multiplied (.2)(.2)(.2), you would end up with .008 (re: Answer A) - but this is clearly SMALLER than the product that will actually occur (because two of those .2s are actually .8s), so the correct answer CANNOT be A.

Final Answer: B

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Rich

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Matt@VeritasPrep GMAT Instructor
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Sun Aug 06, 2017 11:13 pm
We need

(Saturday no rain) * (Sunday no rain) * (Monday YES rain) =>

.8 * .8 * .2 =>

.128

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Jeff@TargetTestPrep GMAT Instructor
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Wed Aug 09, 2017 12:37 pm
AbeNeedsAnswers wrote:
On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

A. 0.008
B. 0.128
C. 0.488
D. 0.512
E. 0.640

B
Since we need to determine the probability that Malachi will return home at the end of the day on the following Monday, we must determine:

P(no rain Sat and no rain Sun and rain Mon) = P(no rain Sat) x P(no rain Sun) x P(rain Mon)

Since the probability of rain is 0.2, the probability of no rain is 1 - 0.2 = 0.8, and thus:

P(no rain Sat) x P(no rain Sun) x P(rain Mon) = 0.8 x 0.8 x 0.2 = 0.128

Answer: B

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