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# On average, a sharpshooter hits the target once every 3 shots. What

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Math Expert
Joined: 02 Sep 2009
Posts: 55230
On average, a sharpshooter hits the target once every 3 shots. What  [#permalink]

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16 Apr 2019, 21:40
00:00

Difficulty:

55% (hard)

Question Stats:

47% (01:43) correct 53% (01:11) wrong based on 34 sessions

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On average, a sharpshooter hits the target once every 3 shots. What is the probability that he will hit the target in 4 shots?

(A) 1
(B) 1/81
(C) 1/3
(D) 65/81
(E) 71/81

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On average, a sharpshooter hits the target once every 3 shots. What  [#permalink]

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Updated on: 16 Apr 2019, 22:57
Bunuel wrote:
On average, a sharpshooter hits the target once every 3 shots. What is the probability that he will hit the target in 4 shots?

(A) 1
(B) 1/81
(C) 1/3
(D) 65/81
(E) 71/81

hiting target 1/3
missing 1-1/3 ; 2/3
so in 4 shots
1-(2/3)^3
1-16/81
65/81
IMO D
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Originally posted by Archit3110 on 16 Apr 2019, 22:27.
Last edited by Archit3110 on 16 Apr 2019, 22:57, edited 1 time in total.
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On average, a sharpshooter hits the target once every 3 shots. What  [#permalink]

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16 Apr 2019, 22:54
1
2
P(hitting the target) = $$\frac{1}{3}$$

P(not hitting the target) = $$\frac{2}{3}$$

P(hitting the target in 4 shots) = 1 - P(not hitting the target in 4 shots)

= $$1 - (\frac{2}{3}*\frac{2}{3}*\frac{2}{3}*\frac{2}{3})$$

= $$1 - \frac{16}{81}$$

= $$\frac{65}{81}$$

OPTION: D
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Re: On average, a sharpshooter hits the target once every 3 shots. What  [#permalink]

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18 Apr 2019, 03:54
Archit3110 wrote:
Bunuel wrote:
On average, a sharpshooter hits the target once every 3 shots. What is the probability that he will hit the target in 4 shots?

(A) 1
(B) 1/81
(C) 1/3
(D) 65/81
(E) 71/81

hiting target 1/3
missing 1-1/3 ; 2/3
so in 4 shots
1-(2/3)^3
1-16/81
65/81
IMO D

Hi, i have a doubt, according to the question, "On average, a sharpshooter hits the target once every 3 shots". So by 3rd shot, he must have hit once and by 4th shot too he must have hit atleast once. Why is the answer not 1 then?
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Re: On average, a sharpshooter hits the target once every 3 shots. What  [#permalink]

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21 Apr 2019, 16:11
I got B.

(1/3)^4=1/81. Can anyone help why this is not correct? Appreciate it.
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Posts: 64
Re: On average, a sharpshooter hits the target once every 3 shots. What  [#permalink]

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22 Apr 2019, 03:28
1
Lobna12 wrote:
I got B.

(1/3)^4=1/81. Can anyone help why this is not correct? Appreciate it.

The approach that you have taken means the shooter will hit in every shot, which is not what the question is asking.

Hope it helps.
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Re: On average, a sharpshooter hits the target once every 3 shots. What   [#permalink] 22 Apr 2019, 03:28
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