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M17-36

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M17-36 [#permalink]

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New post 16 Sep 2014, 01:02
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Question Stats:

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The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. \(\frac{1}{10}\)
B. \(\frac{7}{55}\)
C. \(\frac{5}{36}\)
D. \(\frac{7}{50}\)
E. \(\frac{5}{24}\)
[Reveal] Spoiler: OA

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Re M17-36 [#permalink]

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New post 16 Sep 2014, 01:02
Official Solution:

The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. \(\frac{1}{10}\)
B. \(\frac{7}{55}\)
C. \(\frac{5}{36}\)
D. \(\frac{7}{50}\)
E. \(\frac{5}{24}\)

The probability that event A will occur but event B will not = (the probability that event A will occur)*(1 - the probability that event B will occur) = \(\frac{1}{5}(1 - 0.3) = \frac{1}{5}*\frac{7}{10} = \frac{7}{50}\).

Answer: D
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Re: M17-36 [#permalink]

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New post 03 Nov 2014, 07:36
Bunuel wrote:
Official Solution:

The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. \(\frac{1}{10}\)
B. \(\frac{7}{55}\)
C. \(\frac{5}{36}\)
D. \(\frac{7}{50}\)
E. \(\frac{5}{24}\)

The probability that event A will occur but event B will not = (the probability that event A will occur)*(1 - the probability that event B will occur) = \(\frac{1}{5}(1 - 0.3) = \frac{1}{5}*\frac{7}{10} = \frac{7}{50}\).

Answer: D


IS this not a case of conditional probability???????

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Re M17-36 [#permalink]

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New post 20 May 2017, 04:12
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Will the cases change if the events are not mutually exclusive?

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Re: M17-36 [#permalink]

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New post 20 May 2017, 05:32
Vikram_Katti wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Will the cases change if the events are not mutually exclusive?


Could you elaborate your case? If the conditionals change, the result will change.
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Re: M17-36 [#permalink]

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New post 30 May 2017, 06:45
We need to find the probability that event B does not occur given that event A occurs. Probability of A occurring is 0.2 and probability of B not occurring is 0.7. Hence the required probability is 0.7*0.2=0.14 or 14/100 or 7/50. Hence option D.
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Re: M17-36 [#permalink]

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New post 31 May 2017, 23:12
probability of A=1/5
probability that B will not occur=1-3/10=7/10
hence probability =1/5*7/10=7/50

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Re: M17-36 [#permalink]

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New post 08 Sep 2017, 22:36
I find a matrix makes this problem a bit more digestible.
>> !!!

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Re: M17-36 [#permalink]

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New post 13 Nov 2017, 23:03
Bunuel wrote:
The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. \(\frac{1}{10}\)
B. \(\frac{7}{55}\)
C. \(\frac{5}{36}\)
D. \(\frac{7}{50}\)
E. \(\frac{5}{24}\)


Bunuel, if I change the question :

From If event A occurs, the probability that event B will occur is 30%
To The probability that event B will occur is 30% (I eliminate "If event A occurs")

Do we have the same answer?

Thank you
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Re: M17-36 [#permalink]

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New post 14 Nov 2017, 04:18
septwibowo wrote:
Bunuel wrote:
The probability that event A will occur is 20%. If event A occurs, the probability that event B will occur is 30%. What is the probability that event A will occur but event B will not?

A. \(\frac{1}{10}\)
B. \(\frac{7}{55}\)
C. \(\frac{5}{36}\)
D. \(\frac{7}{50}\)
E. \(\frac{5}{24}\)


Bunuel, if I change the question :

From If event A occurs, the probability that event B will occur is 30%
To The probability that event B will occur is 30% (I eliminate "If event A occurs")

Do we have the same answer?

Thank you


If the events are independent, then yes.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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: M17-36   [#permalink] 14 Nov 2017, 04:18
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