On Saturday morning, Malachi will begin a camping vacation

Question

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

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

Bunuel · Accepted Answer

We are looking for the probability of the following even NNR: no rain on first day, no rain on second day, rain on third day (Monday).

P(NNR)=0.8*0.8*0.2=0.128 .

Answer: B.

Bunuel · Answer

As the probability of rain on each day is 0.2 then the probability of not raining on each day is 1-0.2=0.8. So the probability of not raining on first and second days and raining on third day would be  P(NNR)=0.8*0.8*0.2=0.128 .

Answer: B.

Hope it's clear.

prabu · Answer

can you explain it?

/Prabu

prabu · Answer

Hey i understand this.. but i did not get the following line  "Malachi will begin a camping vacation and he will return home at
the end of the first day on which it rains"  what is this first day means here..

Anyway thanks for your time..

/Prabu

Bunuel · Answer

Vacation starts on Saturday and Malachi will return at the first day on which it rains. Question asks what is the probability that Malachi will return on next Monday, or what is the probability that it will rain on Monday (and not on Saturday or Sunday).

Hope it's clear.

JeffTargetTestPrep · Answer

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

BrentGMATPrepNow · Answer

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

Answer: B

EMPOWERgmatRichC · Answer

Hi All,

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

GMAT assassins aren't born, they're made, 
Rich

MathRevolution · Answer

P(Rain) = 0.2

P(NO rain) = 0.8

Return on following Monday from Saturday: Saturday(No rain) * Sunday(No rain) * Monday(Rain)

=> 0.8 * 0. 8 * 0.2 = 0.128

Answer B

AKANSHAs · Answer

on applying the above used concept for this question-The probability that event M will not occur is 0.8 and the probability that event R will not occur is 0.6. If events M and R cannot both occur, which of the following is the probability that either event M or event R will occur?
we are getting wrong answer-(11/25)

EMPOWERgmatRichC · Answer

Hi AKANSHAs, The prompt that you are asking about has been discussed here: https://gmatclub.com/forum/the-probabil ... 20310.html The math behind the two prompts is a bit different from one another, since the 'setups' are different. The prompt you're asking about tells us three Probability-based pieces of information: 1) The probability that Event M will NOT occur is 0.8 2) The probability that Even R will NOT occur is 0.6 3) Events M and R CANNOT BOTH occur. We’re asked for the probability that Event M OR Event R will occur. While these types of probability questions are generally a bit harder in terms of difficulty, this particular prompt includes “causality” (which is a really rare concept in the Quant section) that actually makes the question easier to solve. Normally, individual probabilities have NO impact on one another, but in this prompt, we are told that if Event M happens, then Event R CANNOT happen (meaning that there is an ‘absolute’ here and nothing to calculate). The same situation occurs if Event R happens (re: Event M automatically does NOT happen and there’s nothing to calculate). Thus, there are just a couple of simple calculations to work through: -The probability that Event M happens is 1 – 0.8 = 0.2 -The probability that Event R happens is 1 – 0.6 = 0.4 Thus, the probability that EITHER will happen is 0.2 + 0.4 = 0.6 GMAT Assassins aren’t born, they’re made, Rich

GMATinsight · Answer

Answer: Option B

Video solution by  GMATinsight

https://www.youtube.com/watch?v=Kej3Yuz0OVc

100mitra · Answer

Correct Option : B

Question Stem  Meaning :
- On Saturday Morning, (1st Day) - Malachi Camping Vacation starts
- Malachi will return home   at the end   of the first   day on which it rains  . 
- Probability of 1st - 3 days (Saturday, Sunday, Monday) of vacation the   probability of rain   on   each day is  0.2

To Find  : 
What is the  probability  that 
Malachi will  return home  
at the  end of the day  
on the following  Monday

Formula  : P(Yes) = 1 - P(No)
 Solution : 
1st Day - No Rain = 1 - 0.2 =  0.8 
2nd Day - No Rain = 1 - 02 =  0.8 
3rd Day - if Rain's =  0.2  (Its the day, if rain's, Probability of Malachi return home)

Probability  = 0.8x0.8x0.2 =  0.128  
(if it rains, on end of camping on last day, and Malachi returns to home)

Kimberly77 · Answer

HI  brunel , Couldn't understand the question "what is the probability that Malachi will return home at the end of the day on the following Monday?" 
How is it relate with 1st two days no rain but 3rd day rain? Thanks for your awesome post always and time in advanced.

EMPOWERgmatRichC · Answer

Hi Kimberly77,

This prompt gives us several pieces of information to work with:

1) 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 
2) Malachi will return home at the end of the day on which it first rains (meaning that if it does NOT rain, then Malachi will NOT leave).

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) =

If you multiply those three values together, then you will have the answer.

GMAT assassins aren't born, they're made, 
Rich

Kimberly77 · Answer

Thanks  EMPOWERgmatRichC  for your reply.
So because question stated Malachi will return home at the end of the first day on which it rains. Therefore we are presuming here only Monday will rain and the others two are no rain? Am I understanding correctly here? Thanks

EMPOWERgmatRichC · Answer

Hi Kimberly77,

Yes - for Malachi to return on Monday, it should NOT rain on Saturday AND NOT on Sunday - AND it must rain on Monday.

GMAT assassins aren't born, they're made, 
Rich

Elite097 · Answer

GMATinsight   EMPOWERgmatRichC   ScottTargetTestPrep   JeffTargetTestPrep  stupid doubt but why do we not divide by 2! since we have NNR and order of first two does not matter

GMATinsight · Answer

It's not a stupid doubt.

The thing is we are not taking the order in account when we calculate the answer using 0.8*0.8*0.2

Understand that we are calculating the probability of a fixed outcome.

Since there are no repetition concerning the arrangement of like events therefore there is no need to exclude the repeated arrangement hence no need to divide by 2!

For instance, Probability of 3 days outcome one which 2 days rain and one day does  = 0.8*0.8*0.2*(\frac{3!}{2!})

But this outcome will have only three results because 0.2 probability could be placed at first, second or third positions while in our question there is only one outcome as 0.2 is placed on last place

I hope it explained the doubt  Elite097

On Saturday morning, Malachi will begin a camping vacation

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On Saturday morning, Malachi will begin a camping vacation

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