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

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Math Expert
Joined: 02 Sep 2009
Posts: 62286
In a shooting contest, each participant only shoots one times. There a  [#permalink]

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13 Feb 2020, 06:56
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Difficulty:

35% (medium)

Question Stats:

75% (01:18) correct 25% (01:30) wrong based on 40 sessions

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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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Joined: 07 May 2019
Posts: 388
Location: India
Re: In a shooting contest, each participant only shoots one times. There a  [#permalink]

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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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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
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9874
Location: United States (CA)
Re: In a shooting contest, each participant only shoots one times. There a  [#permalink]

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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

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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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