OG-17 Problem solving

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Joy Shaha: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Thu May 05, 2016 4:20 am; Thanked: 3 times

by Joy Shaha » Mon Jan 23, 2017 11:09 am

Q. 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 one of the first
three days of the vacation the probability of rain o 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

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Source: Beat The GMAT — Problem Solving | Mon Jan 23, 2017 11:09 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Jan 23, 2017 11:13 am

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

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

Brent Hanneson - Creator of GMATPrepNow.com

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Tue Jan 24, 2017 4:33 am

Joy Shaha wrote:Q. 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 one of the first
three days of the vacation the probability of rain o 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

You can also just use a little logic here. The probability of rain on all three days would be .2^3 = .008. But if it rained on all 3 days, he'd have gone home after the first day, so that can't be right. And the probability of rain on any particular day is .2. If the probability of rain on Monday is .2, the answer must be less than .2, as other stuff needs to happen, so we'll be multiplying .2 by a number less than 1. The only answer greater than .008 and less than .2 is B

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8138; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Jan 27, 2017 9:41 am

Joy Shaha wrote:Q. 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 one of the first
three days of the vacation the probability of rain o 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

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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