Question

P, Q and R were trying to hit a target. If P hits the target 5 times in 8 attempts, Q hits it 3 times in 5 attempts and R hits it 2 times in 4 attempts. What is the probability that the target is hit by at least 2 persons​

Answer 1

Step-by-step explanation:

P(A)=

5

4

,P(B)=

4

3

,P(C)=

3

2

P(

A

)=

5

1

,P(

B

)=

4

1

,P(

C

)=

3

1

(a) P(Exactly two hit the target)

P(A∩B∩

C

)+P(

A

∩B∩C)+P(A∩

B

∩C) [∵ A, B, C are independent events]

=

5

4

.

4

3

.

3

1

+

5

1

.

4

3

.

3

2

+

5

4

.

4

1

.

3

2

=

5

1

+

10

1

+

15

2

=

30

13

(b) P(at least two hit the target)

=P(A∩B∩C)+P(A∩B∩

C

)+P(

A

∩B∩C)+P(A∩

B

∩C)

=

5

4

.

4

3

.

3

2

+

30

13

[Using (a)]

=

5

2

+

30

13

=

30

25

=

6

5