A can hit a tanget 3 times out of 4 attempts, B can hit a target 4 times out of 5 attempts. Each is allowed to shoot once. What is the probability that thetarget is hit ?
Answers
Answer:
Fire a volley means that A,BandC all try to hit the target simultaneously.
Two shots hit the target in one of the following ways:
(1) A and B hit and C fails to hit.
(2) A and C hit and B fails to hit.
(3) B and C hit and A fails to hit.
The chance of hitting by A,P(A)=
5
4
and of not hitting by him P(A
′
)=1−
5
4
=
5
1
.
The chance of hitting by B,P(B)=
4
3
and of not hitting by him P(B
′
)=1−
4
3
=
4
1
.
The chance of hitting by C,P(C)=
3
2
and of not hitting by him P(C
′
)=1−
3
2
=
3
1
.
The probability of (1) is P(ABC
′
)=
5
4
×
4
3
×
3
1
=
5
1
.
The probability of (2) is P(ACB
′
)=
5
4
×
3
2
×
4
1
=
15
2
.
The probability of (3) is P(BCA
′
)=
4
3
×
3
2
×
5
1
=
10
1
.
Thus the probability that two shots hit the target is
5
1
+
15
2
+
10
1
=
30
13
.
Step-by-step explanation:
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