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Probabilty Probelms

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Probabilty Probelms

by Ankittalwar » Wed Jul 20, 2011 11:33 pm
1) The acceptance rate at a certain business school is 15% for the first time applicants and 20% for all re- applicants. If David is applying for admission first time this year, what is the probability that he will have to apply no more than twice before he is accepted?

2) There is a 10% chance it won't snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest probability that it will snow and schools will be closed during the winter?

A) 55% B) 60% C) 70% D) 72% E) 80%

3) If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?

A) 1/32 B) 2/25 C) 5/16 D) 8/25 E) 3/4
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by Anurag@Gurome » Wed Jul 20, 2011 11:56 pm
Ankittalwar wrote:1) The acceptance rate at a certain business school is 15% for the first time applicants and 20% for all re- applicants. If David is applying for admission first time this year, what is the probability that he will have to apply no more than twice before he is accepted?
David will have to apply no more than twice before he is accepted means he is either accepted on first application or on the second.

Hence, required probability = Probability that David gets accepted in the first application + Probability that David gets accepted in the second application

Now, probability that David gets accepted in the second application = (Probability that David gets rejected in the first application)*(Probability that David gets accepted in the second application) = (0.85)*(0.20) = 0.17

Hence, required probability = 0.15 + 0.17 = 0.32
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by Anurag@Gurome » Thu Jul 21, 2011 12:01 am
Ankittalwar wrote:2) There is a 10% chance it won't snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest probability that it will snow and schools will be closed during the winter?
There is a 90% chance that it will snow and 80% chance that the schools will be closed.

Hence, greatest probability that it will snow and schools will be closed = minimum of both the chances = 80%

The correct answer is E.
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by Anurag@Gurome » Thu Jul 21, 2011 12:09 am
Ankittalwar wrote:3) If the probability of rain on any given day in Chicago during the summer is 50%, independent of what happens on any other day, what is the probability of having exactly 3 rainy days from July 4 through July 8, inclusive?
July 4 to July 8 = 5 days

We can select 3 days from 5 days in 5C3 = 10 ways
Now probability that it will rain on these three days = (1/2)*(1/2)*(1/2) = 1/8
And probability that it will not rain in the remaining two days = (1/2)*(1/2) = 1/4

Hence, required probability = (10)*(1/8)*(1/4) = 10/32 = 5/16

The correct answer is C.
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by amit2k9 » Thu Jul 21, 2011 1:59 am
well for 2 you can use tabular method.

School open = Sc School closed = !Sc. Likewise for Snow and Not snowing.

thus,

-----Sc----!Sc---

Sn----------?--- 10

!Sn--------------90
----20-----80----100

thus for Sn !SC max value can be =80 as you can see.

Hence E it is.
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by parveen110 » Wed Jan 29, 2014 9:06 pm
Anurag@Gurome wrote:
Ankittalwar wrote:2) There is a 10% chance it won't snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest probability that it will snow and schools will be closed during the winter?
There is a 90% chance that it will snow and 80% chance that the schools will be closed.

Hence, greatest probability that it will snow and schools will be closed = minimum of both the chances = 80%

The correct answer is E.
There's a confusion. Why are we taking minimum of both the chances here. if the events are independent of each other. we should just multiply the events. (8/10)*(9/10)=72%. Please explain.
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by Matt@VeritasPrep » Mon Feb 03, 2014 4:11 pm
The key phrase here is "the greatest chance", which would be if the events are NOT independent. Let's say the odds that it doesn't snow all winter long are A and the odds that the schools will not be closed all winter long are B. If B guarantees A, however, then A is dependent on B and the question "What are the odds that A and B both happen?" is really "What are the odds that B happens?"

Let me know if that makes sense - probability can be really perplexing!
parveen110 wrote:
Anurag@Gurome wrote:
Ankittalwar wrote:2) There is a 10% chance it won't snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest probability that it will snow and schools will be closed during the winter?
There is a 90% chance that it will snow and 80% chance that the schools will be closed.

Hence, greatest probability that it will snow and schools will be closed = minimum of both the chances = 80%

The correct answer is E.
There's a confusion. Why are we taking minimum of both the chances here. if the events are independent of each other. we should just multiply the events. (8/10)*(9/10)=72%. Please explain.
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by GMATGuruNY » Mon Feb 03, 2014 8:20 pm
Ankittalwar wrote: There is a 10% chance it won't snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest probability that it will snow and schools will be closed during the winter?

A) 55% B) 60% C) 70% D) 72% E) 80%
To see the situation more clearly, let's say that -- for all eternity -- the total number of days of winter = 100.

There is a 10% chance it won't snow all winter long.
Thus, during the 100 days of winter, there are 10 days of no snow and 90 days of snow.

There is a 20% chance that schools will not be closed all winter long.
Thus, during the 100 days of winter, there are 20 days when the schools are not closed and 80 days when the schools are closed.

Let S = snow, NS = no snow, C = closed, and NC = not closed.
The result is the following grid:
Image

We want to MAXIMIZE the probability that it will snow and that schools will be closed.
Thus, we must determine the GREATEST POSSIBLE VALUE that could be placed in the top left box, which represents the number of days when it snows and when schools are closed.
Since the total of the top row = 80, the greatest possible value that could be placed in the top left box is 80, yielding the following grid:
Image

Thus, the greatest probability that it will snow and that schools will be closed = 80/100 = 80%.

The correct answer is E.
Last edited by GMATGuruNY on Tue Feb 04, 2014 6:27 am, edited 1 time in total.
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by parveen110 » Tue Feb 04, 2014 6:02 am
Matt@VeritasPrep wrote:The key phrase here is "the greatest chance", which would be if the events are NOT independent. Let's say the odds that it doesn't snow all winter long are A and the odds that the schools will not be closed all winter long are B. If B guarantees A, however, then A is dependent on B and the question "What are the odds that A and B both happen?" is really "What are the odds that B happens?"

Let me know if that makes sense - probability can be really perplexing!
parveen110 wrote:
Anurag@Gurome wrote:
Ankittalwar wrote:2) There is a 10% chance it won't snow all winter long. There is a 20% chance that schools will not be closed all winter long. What is the greatest probability that it will snow and schools will be closed during the winter?
There is a 90% chance that it will snow and 80% chance that the schools will be closed.

Hence, greatest probability that it will snow and schools will be closed = minimum of both the chances = 80%

The correct answer is E.
There's a confusion. Why are we taking minimum of both the chances here. if the events are independent of each other. we should just multiply the events. (8/10)*(9/10)=72%. Please explain.
Hi Matt,
Thanks for the reply. However, i din't quite get your meaning. Could you please explain it more elaborately.
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