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p is the probability of snow fall on any given day in the fi

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p is the probability of snow fall on any given day in the fi [#permalink] New post 30 Oct 2012, 06:56
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p is the probability of snow fall on any given day in the first week of December. If snow fall on one day does not affect the probability of snow fall on any other day, what is the value of p?

(1) The probability that snow will fall on at least one day during the first week of December is .918.

(2) The probability that snow will fall every day during this week is .00022
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Re: p is the probability of snow fall on any given day in the fi [#permalink] New post 30 Oct 2012, 08:15
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p is the probability of snow fall on any given day in the first week of December. If snow fall on one day does not affect the probability of snow fall on any other day, what is the value of p?

(1) The probability that snow will fall on at least one day during the first week of December is .918 --> 0.918=1-P(not snowing on ANY day)=1-(1-p)^7 --> (1-p)^7=0.082 --> we can find the single numerical value of p. Sufficient.

(2) The probability that snow will fall every day during this week is .00022 --> p^7=0.00022 --> we can find the single numerical value of p. Sufficient.

Answer: D.

Hope it's clear.
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Re: p is the probability of snow fall on any given day in the fi [#permalink] New post 30 Oct 2012, 08:16
sanjoo wrote:
p is the probability of snow fall on any given day in the first week of December. If snow fall on one day does not affect the probability of snow fall on any other day, what is the value of p?

(1) The probability that snow will fall on at least one day during the first week of December is .918.

(2) The probability that snow will fall every day during this week is .00022


Statement 1: probability of snow fall on atleast one day =0.918
=> probability of no snow fall in entire week = 1-0.918
=> since snow fall on one day doesnt affect probability on another day, if probability of no snow fall on a day is q, then q^7 = 1-0.918
this would give q and p =1-q
Hence we can find p. Sufficient

Statement 2: probability of snow fall on every day = p^7 =0.00022
this would give p
Hence sufficient.

Ans D it is.
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Re: p is the probability of snow fall on any given day in the fi [#permalink] New post 30 Oct 2012, 08:21
Expert's post
Bunuel wrote:
p is the probability of snow fall on any given day in the first week of December. If snow fall on one day does not affect the probability of snow fall on any other day, what is the value of p?

(1) The probability that snow will fall on at least one day during the first week of December is .918 --> 0.918=1-P(not snowing on ANY day)=1-(1-p)^7 --> (1-p)^7=0.082 --> we can find the single numerical value of p. Sufficient.

(2) The probability that snow will fall every day during this week is .00022 --> p^7=0.00022 --> we can find the single numerical value of p. Sufficient.

Answer: D.

Hope it's clear.


Just noticed that the two statements give two different values of p: 0.300431 and 0.300254. Thus the two statements contradict each other, which never happens on the real test. Not a good question.
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Re: p is the probability of snow fall on any given day in the fi [#permalink] New post 06 Nov 2012, 11:45
Bunuel wrote:
p is the probability of snow fall on any given day in the first week of December. If snow fall on one day does not affect the probability of snow fall on any other day, what is the value of p?

(1) The probability that snow will fall on at least one day during the first week of December is .918 --> 0.918=1-P(not snowing on ANY day)=1-(1-p)^7 --> (1-p)^7=0.082 --> we can find the single numerical value of p. Sufficient.

(2) The probability that snow will fall every day during this week is .00022 --> p^7=0.00022 --> we can find the single numerical value of p. Sufficient.

Answer: D.

Hope it's clear.


not sure whether my understand is rite here.. just correct me if I am wrong..

why we represent not snowing on any day as (1-p)^7 instead of P. Is that since we are calcuating for 7 days in a week?
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Re: p is the probability of snow fall on any given day in the fi [#permalink] New post 07 Nov 2012, 04:41
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breakit wrote:
Bunuel wrote:
p is the probability of snow fall on any given day in the first week of December. If snow fall on one day does not affect the probability of snow fall on any other day, what is the value of p?

(1) The probability that snow will fall on at least one day during the first week of December is .918 --> 0.918=1-P(not snowing on ANY day)=1-(1-p)^7 --> (1-p)^7=0.082 --> we can find the single numerical value of p. Sufficient.

(2) The probability that snow will fall every day during this week is .00022 --> p^7=0.00022 --> we can find the single numerical value of p. Sufficient.

Answer: D.

Hope it's clear.


not sure whether my understand is rite here.. just correct me if I am wrong..

why we represent not snowing on any day as (1-p)^7 instead of P. Is that since we are calcuating for 7 days in a week?


The probability of snowing is p, thus the probability of not snowing is 1-p.
The probability of not snowing entire week is (1-p)^7, therefore the probability of snowing on at least one day is 1-(1-p)^7.

Hope it's clear.
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p is the probability of snow fall on any given day [#permalink] New post 28 Jan 2013, 16:30
p is the probability of snow fall on any given day in the first week of December. If snow fall on one day does not affect the probability of snow fall on any other day, what is the value of p?

(1) The probability that snow will fall on at least one day during the first week of December is .918.

(2) The probability that snow will fall every day during this week is .00022

I have two doubts about the wording of this question:
a) When the question says "p is the probability of snow fall on any given day in the first week of December" , it means that the probability of snow fall on Monday is p, on Tuesday is p, on wednesday the same, ..., right?
b) In the statement (2), I think that "this week" is not clear. Which "this week"?, the first week of december or the current week? I don't think that a real GMAT question would use "this week". What do you think?
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Re: p is the probability of snow fall on any given day [#permalink] New post 28 Jan 2013, 16:37
Expert's post
danzig wrote:
p is the probability of snow fall on any given day in the first week of December. If snow fall on one day does not affect the probability of snow fall on any other day, what is the value of p?

(1) The probability that snow will fall on at least one day during the first week of December is .918.

(2) The probability that snow will fall every day during this week is .00022

I have two doubts about the wording of this question:
a) When the question says "p is the probability of snow fall on any given day in the first week of December" , it means that the probability of snow fall on Monday is p, on Tuesday is p, on wednesday the same, ..., right?
b) In the statement (2), I think that "this week" is not clear. Which "this week"?, the first week of december or the current week? I don't think that a real GMAT question would use "this week". What do you think?


Please refer to the solutions above and ask if anything remains unclear.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: p is the probability of snow fall on any given day in the fi [#permalink] New post 29 Jan 2013, 14:07
Statement 1: Probability of snowing on "at least 1 day" = (1 - probability of snowing on zero days). Since there is only one unknown we can rearrange the equation to solve for p. Sufficient.

Statement 2: Since .00022 is the probability of snowing everyday, p^7 must equal 0.00022. We can backsolve to get p. Sufficient.
Re: p is the probability of snow fall on any given day in the fi   [#permalink] 29 Jan 2013, 14:07
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