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In a shooting contest, each participant only shoots one times. There a

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In a shooting contest, each participant only shoots one times. There a  [#permalink]

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New post 13 Feb 2020, 06:56
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In a shooting contest, each participant only shoots one times. There are 3 participants A, B and C. The probability that A, B and C hit the target are 0.7, 0.6 and 0.5 respectively. What is the probability that there is at least one participant who hits the target?

A. 0.45
B. 0.75
C. 0.79
D. 0.8
E. 0.94

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Re: In a shooting contest, each participant only shoots one times. There a  [#permalink]

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New post 13 Feb 2020, 10:23
Bunuel wrote:
In a shooting contest, each participant only shoots one times. There are 3 participants A, B and C. The probability that A, B and C hit the target are 0.7, 0.6 and 0.5 respectively. What is the probability that there is at least one participant who hits the target?

A. 0.45
B. 0.75
C. 0.79
D. 0.8
E. 0.94


Solution.


    • Probability of A hitting the target = \(0.7\).
      o Probability of A not hitting the target = \(1 – 0 7 = 0.3\).
    • Probability of B hitting the target = \(0.6\)
      o Probability of B not hitting the target = \(1 – 0.6 = 0.4\).
    • Probability of C hitting the target =\( 0.5\)
      o Probability of C not hitting the target = \(1-0.5=0.5\)
    • There are four cases:
      o Case I: None of them hitting the target.
      o Case 2: Exactly one of them hitting the target.
      o Case 3: Exactly two of them hitting the target.
      o Case 4: All of them hit the target.
    • Case 2, 3, and 4 are favourable case.
      o Probability of none of them hitting the target= P(A not hitting)*P(B not hitting)*P(C not hitting)=\(0.3*0.4*0.5=0.06\)
    • P(at least one of them hitting the target)=\(1- P(none\ of\ them\ hitting\ the\ target)=1-0.06=0.94\)
Hence, the correct answer is Option E.
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Re: In a shooting contest, each participant only shoots one times. There a  [#permalink]

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New post 14 Feb 2020, 07:07
not hitting target ; .3,.4 .5
the probability that there is at least one participant who hits the target
1-(.3*.4*.5) ; .94
IMO E

Bunuel wrote:
In a shooting contest, each participant only shoots one times. There are 3 participants A, B and C. The probability that A, B and C hit the target are 0.7, 0.6 and 0.5 respectively. What is the probability that there is at least one participant who hits the target?

A. 0.45
B. 0.75
C. 0.79
D. 0.8
E. 0.94
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Joined: 14 Oct 2015
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Re: In a shooting contest, each participant only shoots one times. There a  [#permalink]

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New post 21 Feb 2020, 08:07
1
Bunuel wrote:
In a shooting contest, each participant only shoots one times. There are 3 participants A, B and C. The probability that A, B and C hit the target are 0.7, 0.6 and 0.5 respectively. What is the probability that there is at least one participant who hits the target?

A. 0.45
B. 0.75
C. 0.79
D. 0.8
E. 0.94


We can use the formula:

P(at least one person hitting the target) = 1 - P(no people hitting the target)

Thus:

1 - P(no people hitting the target) = 1 - (0.3 x 0.4 x 0.5) = 1 - 0.06 = 0.94

Answer: E
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Re: In a shooting contest, each participant only shoots one times. There a   [#permalink] 21 Feb 2020, 08:07
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