Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: Rain at least 3 days [#permalink]
21 Aug 2010, 16:19

ichha148 wrote:

If the probability of rain on any given day is 50%, what is the probability that it will rain on at least 3 days in a row during a 5 day period? (A) 3/32

(B) 1/4

(C) 9/32

(D)5/16

(E) 1/2

Please explain . OA to be shared later

My attempt:

Rainy days - R, Non-Rainy days - NR.

Prob of at least 3 rainy days - 1 - (Prob of zero + Prob of 1 + Prob of 2 rainy days)

Prob of zero rainy days - NNNNN - \(1/(2^5)\)

Prob of 1 rainy day - NNNNR - \(1/(2^5)\). But the one rainy day could be either first, second of third...

Hence total combination - \(5C1\). Prob of 1 rainy day - \(5 * 1/(2^5)\)

Prob of 2 rainy day - NNNRR - \(1/(2^5)\). But the one rainy day could be either first & second or third & fourth...

Hence total combination - 5C2. Prob of 1 rainy day - \(10 * 1/(2^5)\)

Re: Rain at least 3 days [#permalink]
21 Aug 2010, 19:33

5

This post received KUDOS

Expert's post

4

This post was BOOKMARKED

ichha148 wrote:

If the probability of rain on any given day is 50%, what is the probability that it will rain on at least 3 days in a row during a 5 day period? (A) 3/32

Veritas Combinatorics and Probability Question #12 [#permalink]
27 Apr 2011, 18:16

I am reviewing the Veritas Combinatorics and Probability book right now and have a question on question 12 (pg 54). It asks: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least 3 days in a row during a 5 day period?

I understand the explanation given in the book. The method is a little tedious--it solves the problem by drawing out all the possibilities and then adding them together. Anyone know how to solve this by pure math/combinatorics instead of writing out all the possibilities?

Conversely you can use the 1- x rule. P(at least 3 days ) = 1- P(atmost 2 days)

gmatstudier wrote:

I am reviewing the Veritas Combinatorics and Probability book right now and have a question on question 12 (pg 54). It asks: If the probability of rain on any given day is 50%, what is the probability that it will rain on at least 3 days in a row during a 5 day period?

I understand the explanation given in the book. The method is a little tedious--it solves the problem by drawing out all the possibilities and then adding them together. Anyone know how to solve this by pure math/combinatorics instead of writing out all the possibilities?

I just came across a similar problem where instead of EXACTLY 3 out of 5 days rain it says AT LEAST 3 out of 5 days rain. So you would have to calculate the chance of rain occurring on 3, 4, and 5 days:

You would do (5C3 + 5C4 + 5C5) / 2^5

16/32 = 1/2

Testluv, for the pascal's triangle in this situation you would go to the last row and add everything to the right of the 3rd digit 10 (Digit 4, 5, and 6)? so 10 + 5 + 1 = 16/32? Yes, that's correct. (Alernatively, you can go to the last row, and add everything to the left of the fourth digit: 1 + 5 + 10 = 16.)

EDIT: Here's how we work with the last row. If asked for probability of 0 rainy days (or 0 heads, etc), then we look at either the "1" that begins the row or the "1" that ends the row. If we want to 1 rainy day, then we look at either of the "5"s. If we want 2 or 3 rainy days, then we look at either of the "10"s. If we want "at least" then we just sum up in the manner you intuited.

When a probability problem says "at least" it is almost always easier to think about the undesirable events, and then subtract from 1. So, using the formula, it would be easier to say: 1 - (5C0 + 5C1 + 5C2)/2^5 = 1/2. Here, it doesn't make a big difference but if the problem had said "at least 2 days of rain", it would be far quicker to compute 5C0 + 5C1, than it would be to compute 5C2 + 5C3 + 5C4 + 5C5.

Know that nCn = nC0 = 1. Also, nC1 = n. Knowing this greatly speeds up usage of the formula.

gmatstudier wrote:

Yeah that's what I thought, but the answer is .25. I tried adding your equation up and it didn't match. Am I doing somehting wrong?

Re: Veritas Combinatorics and Probability Question #12 [#permalink]
27 Apr 2011, 19:40

1

This post received KUDOS

Expert's post

It's not asking for the probability that it rains on any 3 (or more) days; it's asking for the probability it rains on (at least) 3 days *in a row*. That's going to be less likely than it just raining on 3 days, because we don't want to count some sequences, like Rain, Sun, Rain, Sun, Rain, where we don't have 3 rainy days in a row.

There are a lot of ways to count the sequences which have 3 Rs in a row. Let's think of a sequence of rainy and sunny days as a word containing R's and S's. We can count as follows:

* if our word starts with RRR, we'd have 2 choices for the fourth and fifth days, so 2*2 = 4 sequences which begin with three rainy days

* if our word starts with SRRR, we have 2 choices for the final day, for 2 sequences we haven't yet counted with three rainy days in the middle (we have already counted the possibilities where the first day is an R)

* if our word ends in RRR, we have 2 final possibilities we have not yet counted: RSRRR and SSRRR (we have counted the possibilities with three Rs in the middle, so we need to make sure only to count those possibilities where the second day is an S)

so, adding, there are a total of 8 sequences with at least three consecutive Rs, and since there are 2^5 = 32 total sequences, the probability of having at least three consecutive rainy days is 8/32 = 1/4. _________________

GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

Re: tough probability question from veritas [#permalink]
04 Oct 2013, 20:32

eeakkan wrote:

ıf the probability of rain on any given day is 50%, what is the probability that it will rain on at least 3 days ina row during a 5 days period? a) 3/32 b) 1/4 c) 9/32 d) 5/16 e) 1/2

Bunuel please help me with this question. Because I have not understand the answer.

See.. the Possibility of Rain on any given day=1/2

Now lets take the 5 day period...

Now we want to make it rain for 3 continuous days so : 1.1.1.1/2.1/2 for rain can happen or not for last 2 days of the week

Re: Rain at least 3 days [#permalink]
08 Oct 2013, 05:43

Bunuel wrote:

ichha148 wrote:

If the probability of rain on any given day is 50%, what is the probability that it will rain on at least 3 days in a row during a 5 day period? (A) 3/32

Re: Rain at least 3 days [#permalink]
08 Oct 2013, 05:49

Expert's post

pauc wrote:

Bunuel wrote:

ichha148 wrote:

If the probability of rain on any given day is 50%, what is the probability that it will rain on at least 3 days in a row during a 5 day period? (A) 3/32

Why did you add up the probabilities of the 3 scenarios vs. get the product of the 3 (5/16)?

Let me ask you a question: the probability of heads is 1/2, the probability of tails is also 1/2. What is the probability of getting a head OR a tail when flipping once? Is it 1/2+1/2=1 or 1/2*1/2=1/4? _________________

Re: Rain at least 3 days [#permalink]
08 Oct 2013, 06:33

Bunuel wrote:

Let me ask you a question: the probability of heads is 1/2, the probability of tails is also 1/2. What is the probability of getting a head OR a tail when flipping once? Is it 1/2+1/2=1 or 1/2*1/2=1/4?

Won't it be just 1/2? But I get what you mean when the probability problem is an OR/AND problem. I just get confused sometimes as to which of the 2 it is, especially if the problem doesn't explicitly state if it's an OR or an AND problem.

Re: Rain at least 3 days [#permalink]
08 Oct 2013, 06:36

Expert's post

pauc wrote:

Bunuel wrote:

Let me ask you a question: the probability of heads is 1/2, the probability of tails is also 1/2. What is the probability of getting a head OR a tail when flipping once? Is it 1/2+1/2=1 or 1/2*1/2=1/4?

Won't it be just 1/2? But I get what you mean when the probability problem is an OR/AND problem. I just get confused sometimes as to which of the 2 it is, especially if the problem doesn't explicitly state if it's an OR or an AND problem.

The probability of getting either tails or heads is 100%. How else? _________________

Re: If the probability of rain on any given day is 50%, what is [#permalink]
28 Oct 2014, 03:25

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Hello everyone! Researching, networking, and understanding the “feel” for a school are all part of the essential journey to a top MBA. Wouldn’t it be great... ...

As part of our focus on MBA applications next week, which includes a live QA for readers on Thursday with admissions expert Chioma Isiadinso, we asked our bloggers to...