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

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SOURH7WK
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The probability of a man hitting a bulls eye in one fire is [#permalink] New post  Updated on: 07 Aug 2012, 07:10
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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
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Originally posted by SOURH7WK on 07 Aug 2012, 06:49.
Last edited by SOURH7WK on 07 Aug 2012, 07:10, edited 2 times in total.
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mandyrhtdm
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Re: The probability of a man hitting a bulls eye in one fire is [#permalink] New post  07 Aug 2012, 09:13
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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.
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Bunuel
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Re: The probability of a man hitting a bulls eye in one fire is [#permalink] New post  07 Aug 2012, 07:05
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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.

Answer: C.

P.S. You must indicate OA, rule #7: rules-for-posting-please-read-this-before-posting-133935.html
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Re: The probability of a man hitting a bulls eye in one fire is [#permalink] New post  08 Aug 2012, 10:20
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] New post  30 May 2019, 03:56
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.

Answer: C.

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?

Please explain.

Thanks,
Bhavana
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Bunuel
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Re: The probability of a man hitting a bulls eye in one fire is [#permalink] New post  30 May 2019, 04:00
Expert Reply
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.

Answer: C.

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?

Please explain.

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] New post  30 May 2019, 09:27
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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
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Re: The probability of a man hitting a bulls eye in one fire is [#permalink] New post  12 Mar 2024, 05:44
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