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# The probability of a man hitting a bulls eye in one fire is

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Senior Manager
Joined: 15 Jun 2010
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Schools: IE'14, ISB'14, Kellogg'15
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The probability of a man hitting a bulls eye in one fire is  [#permalink]

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Updated on: 07 Aug 2012, 06:10
5
13
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:53) correct 32% (02:14) wrong based on 216 sessions

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The probability of a man hitting a bulls eye in one fire is 1/4. What is the least number of times that the man should fire in order to take the probability of hitting the bulls eye at least once to more than 50%.

A. 5
B. 7
C. 3
D. 12
E. 6

Originally posted by SOURH7WK on 07 Aug 2012, 05:49.
Last edited by SOURH7WK on 07 Aug 2012, 06:10, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 62353
Re: The probability of a man hitting a bulls eye in one fire is  [#permalink]

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07 Aug 2012, 06:05
4
1
SOURH7WK wrote:
The probability of a man hitting a bulls eye in one fire is 1/4. What is the least number of times that the man should fire in order to take the probability of hitting the bulls eye at least once to more than 50%.

A. 5
B. 7
C. 3
D. 12
E. 6

OA will follow after few discussions

The probability that the man hits the bulls eye at least once in 2 tries is 1-(3/4)^2=7/16, so less than 1/2 (the probability of hitting the bulls eye at least once is 1 minus the probability of the opposite event, so the probability that the men misses in all 2 tries).

The probability that the man hits the bulls eye at least once in 3 tries is 1-(3/4)^3=37/64, so more than 1/2.

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Re: The probability of a man hitting a bulls eye in one fire is  [#permalink]

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07 Aug 2012, 08:13
6
5
SOURH7WK wrote:
The probability of a man hitting a bulls eye in one fire is 1/4. What is the least number of times that the man should fire in order to take the probability of hitting the bulls eye at least once to more than 50%.

A. 5
B. 7
C. 3
D. 12
E. 6

It is a Typical Probability Question
IN Probability we have a rule ( which is logic actually) that
P(>1) = 1-P(0)
That is Probability of hitting the bulls eye at least once out of N trials is 1- probability of missing it all the times. & P of missing it is 3/4

That means$$1-(\frac{3}{4})^n$$ > $$\frac{1}{2}$$

Solve it , n > 3 satisfies.
##### General Discussion
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Re: The probability of a man hitting a bulls eye in one fire is  [#permalink]

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08 Aug 2012, 09:20
very helpful Bunuel/mandyr, need to revise the "at least" rule and this helps, thank you both
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The probability of a man hitting a bulls eye in one fire is  [#permalink]

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30 May 2019, 02:56
Bunuel wrote:
SOURH7WK wrote:
The probability of a man hitting a bulls eye in one fire is 1/4. What is the least number of times that the man should fire in order to take the probability of hitting the bulls eye at least once to more than 50%.

A. 5
B. 7
C. 3
D. 12
E. 6

OA will follow after few discussions

The probability that the man hits the bulls eye at least once in 2 tries is 1-(3/4)^2=7/16, so less than 1/2 (the probability of hitting the bulls eye at least once is 1 minus the probability of the opposite event, so the probability that the men misses in all 2 tries).

The probability that the man hits the bulls eye at least once in 3 tries is 1-(3/4)^3=37/64, so more than 1/2.

Hi Bunuel ,

In question it is mentioned that " at least once to more than 50%", is that the reason you have checked if the probability value is greater than or less than 1/2?

Thanks,
Bhavana
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Thanks,
Bhavana
Math Expert
Joined: 02 Sep 2009
Posts: 62353
Re: The probability of a man hitting a bulls eye in one fire is  [#permalink]

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30 May 2019, 03:00
bhavana31 wrote:
Bunuel wrote:
SOURH7WK wrote:
The probability of a man hitting a bulls eye in one fire is 1/4. What is the least number of times that the man should fire in order to take the probability of hitting the bulls eye at least once to more than 50%.

A. 5
B. 7
C. 3
D. 12
E. 6

OA will follow after few discussions

The probability that the man hits the bulls eye at least once in 2 tries is 1-(3/4)^2=7/16, so less than 1/2 (the probability of hitting the bulls eye at least once is 1 minus the probability of the opposite event, so the probability that the men misses in all 2 tries).

The probability that the man hits the bulls eye at least once in 3 tries is 1-(3/4)^3=37/64, so more than 1/2.

Hi Bunuel ,

In question it is mentioned that " at least once to more than 50%", is that the reason you have checked if the probability value is greater than or less than 1/2?

Thanks,
Bhavana

Yes, more than 50% means more than 1/2.
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Re: The probability of a man hitting a bulls eye in one fire is  [#permalink]

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30 May 2019, 08:27
3
SOURH7WK wrote:
The probability of a man hitting a bulls eye in one fire is 1/4. What is the least number of times that the man should fire in order to take the probability of hitting the bulls eye at least once to more than 50%.

A. 5
B. 7
C. 3
D. 12
E. 6

1/4 * x >50/100
or say
x>2
IMO C; 3
Re: The probability of a man hitting a bulls eye in one fire is   [#permalink] 30 May 2019, 08:27
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