probability

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smagish: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Mon Jun 18, 2012 10:32 pmFollowed by: 1 member; Thanked: 1 times

by smagish » Sat Aug 18, 2012 12:48 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

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Source: Beat The GMAT — Problem Solving | Sat Aug 18, 2012 12:48 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sat Aug 18, 2012 1:07 am

Malachi returns at the end of the first day on which it rains.
For him to return at the end of monday, monday should be the frst day when it rains

Probability that it doesn't rain on Saturday = 1-0.2 = 0.8
Probability that it doesn't rain on Sunday = 1-0.2 = 0.8
Probability that it rains on Monday = 0.2
Probability that it rains on monday and not on sat and sun = 0.8*0.8*0.2 = 0.128

Option B

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sat Aug 18, 2012 4:31 am

smagish 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

This question is the way-way difficult to get an answer rather reading from the proposed solution by riju The question can be solved with 100% guarantee of correctness if we use binomial probability distribution for a series of 'success'-'failure' events given P(failure=rain) is always the same 0.2

Thus, 3C1*(0.2)*(0.8)^2=0.384. This will be the sum of all possible events: Rain-Not Rain-Not Rain, Not Rain-Rain-Not Rain, Not Rain-Not Rain-Rain.

If you look into the condition I underscored in quote you should notice that the first two options in a series of events are locked (switched off). Hence we are left only with 0.128 which is 0.384/3 the third option.

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Sat Aug 18, 2012 5:58 am

pemdas wrote:
smagish 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
This question is the way-way difficult to get an answer rather reading from the proposed solution by riju The question can be solved with 100% guarantee of correctness if we use binomial probability distribution for a series of 'success'-'failure' events given P(failure=rain) is always the same 0.2

Thus, 3C1*(0.2)*(0.8)^2=0.384. This will be the sum of all possible events: Rain-Not Rain-Not Rain, Not Rain-Rain-Not Rain, Not Rain-Not Rain-Rain.

If you look into the condition I underscored in quote you should notice that the first two options in a series of events are locked (switched off). Hence we are left only with 0.128 which is 0.384/3 the third option.

I don't understand how you got to the formula 3C1*(0.2)*(0.8)^2=0.384
Can you explain in a little more detail?

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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 » Sat Aug 18, 2012 7:24 am

smagish 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

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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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Sat Aug 18, 2012 12:33 pm

rijul007 wrote: I don't understand how you got to the formula 3C1*(0.2)*(0.8)^2=0.384
Can you explain in a little more detail?

stats:binomial probability
n= #trials
k= #successes
n-k= #failures
p= P(success)
q= P(failure)=1-q

nCk * (p^k) * (q^n-k)

n= 3
k= 1
p= 0.2
q= 0.8
3C1*(0.2)*(0.8)^2=0.384
for general reference, you can look up https://www.mathwords.com/b/binomial_pro ... ormula.htm

Success doesn't come overnight!

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nailGmat2012: Senior | Next Rank: 100 Posts; Posts: 33; Joined: Wed Jan 11, 2012 5:18 pm

by nailGmat2012 » Sun Aug 19, 2012 8:23 am

I don't understand how you got to the formula 3C1*(0.2)*(0.8)^2=0.384
Can you explain in a little more detail?

forget the original question.
If the question was: If the probability of rain on any given day is 0.2 what's the probability that it will rain exactly once in the next three days.

probability of raining any one day (only) in three days = 0.2 * 0.8 * 0.8
Now choose 1 day from the 3 days it can happen = 3C1

probability that it will rain exactly once in the next three days = 3C1 * 0.2 * 0.8 * 0.8 = 3C1*(0.2)*(0.8)^2=0.384

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