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The probability of Jack hitting the bull’s eye is 40%. How many times

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The probability of Jack hitting the bull’s eye is 40%. How many times [#permalink]

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The probability of Jack hitting the bull’s eye is 40%. How many times should he throw the dart in order to have more than 90% probability of hitting the bull’s eye at least once?

A. 3
B. 4
C. 5
D. 6
E. 7
[Reveal] Spoiler: OA

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Re: The probability of Jack hitting the bull’s eye is 40%. How many times [#permalink]

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New post 23 Oct 2017, 01:02
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nkmungila wrote:
The probability of Jack hitting the bull’s eye is 40%. How many times should he throw the dart in order to have more than 90% probability of hitting the bull’s eye at least once?

A. 3
B. 4
C. 5
D. 6
E. 7


For n throws the probability of hitting the bull’s eye at least once is 1 - P(not hitting at all in n throws) = 1 - (0.6)^n = 1 - (3/5)^n. We need this value to be greater than 90%:

1 - (3/5)^n > 9/10;

1/10 > (3/5)^n.

The least value of n is 5.

Answer: C.
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Re: The probability of Jack hitting the bull’s eye is 40%. How many times [#permalink]

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New post 26 Oct 2017, 15:31
nkmungila wrote:
The probability of Jack hitting the bull’s eye is 40%. How many times should he throw the dart in order to have more than 90% probability of hitting the bull’s eye at least once?

A. 3
B. 4
C. 5
D. 6
E. 7


Since the probability of Jack’s hitting the bull’s-eye is 40%, the probability that he doesn’t hit the bull’s-eye is 60%, or 0.6. The probability that he will hit the bull’s-eye at least once is 1 - (probability that he will not hit the bull’s-eye)^n, where n is the number of times that he will not hit the bull’s-eye. Thus, we want:

1 - 0.6^n > 0.9

-0.6^n > -0.1

0.6^n < 0.1

Since 0.6^4 = 0.1296 and 0.6^5 = 0.07776, n = 5.

Answer: C
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Re: The probability of Jack hitting the bull’s eye is 40%. How many times [#permalink]

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New post 30 Oct 2017, 14:07
Bunuel wrote:
nkmungila wrote:
The probability of Jack hitting the bull’s eye is 40%. How many times should he throw the dart in order to have more than 90% probability of hitting the bull’s eye at least once?

A. 3
B. 4
C. 5
D. 6
E. 7


For n throws the probability of hitting the bull’s eye at least once is 1 - P(not hitting at all in n throws) = 1 - (0.6)^n = 1 - (3/5)^n. We need this value to be greater than 90%:

1 - (3/5)^n > 9/10;

1/10 > (3/5)^n.

The least value of n is 5.

Answer: C.


Hello Bunuel, thanks for the explanation. I understand the logic, but once you have identified that the key is to find n so that 1/10 > (3/5)^n ... is there a quick shortcut for doing the calculations that i am not seeing?

Thanks a lot for your support!

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Re: The probability of Jack hitting the bull’s eye is 40%. How many times [#permalink]

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New post 30 Oct 2017, 23:39
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delid wrote:
Bunuel wrote:
nkmungila wrote:
The probability of Jack hitting the bull’s eye is 40%. How many times should he throw the dart in order to have more than 90% probability of hitting the bull’s eye at least once?

A. 3
B. 4
C. 5
D. 6
E. 7


For n throws the probability of hitting the bull’s eye at least once is 1 - P(not hitting at all in n throws) = 1 - (0.6)^n = 1 - (3/5)^n. We need this value to be greater than 90%:

1 - (3/5)^n > 9/10;

1/10 > (3/5)^n.

The least value of n is 5.

Answer: C.


Hello Bunuel, thanks for the explanation. I understand the logic, but once you have identified that the key is to find n so that 1/10 > (3/5)^n ... is there a quick shortcut for doing the calculations that i am not seeing?

Thanks a lot for your support!


You can find it by trial and error.

1/10 is an easy fraction for comparison and 3/5 = 6/10, so it should not be hard to do.
_________________

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.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: The probability of Jack hitting the bull’s eye is 40%. How many times [#permalink]

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New post 30 Nov 2017, 14:17
Probability of hitting bull's eye per attempt= 0.4

Therefore, probability of not hitting bull's eye per attempt= 1-0.4= 0.6

The question is basically asking us to calculate number of attempts required to bring this "probability of not hitting bull's eye" to <=0.1

One Attempt, P(no bull's eye)=0.6

Two Attempts= 0.6*0.6=0.36

Three Attempts= 0.216

Four Attempts= 0.1296

So, we need five attempts to bring down "probability of not hitting bull's eye" to below 0.1

Hence, Ans C

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Re: The probability of Jack hitting the bull’s eye is 40%. How many times   [#permalink] 30 Nov 2017, 14:17
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