In shooting arena there are 5 different guns. Probability of hitting a

danrussekme

danrussekme

Answered question

2021-11-16

In shooting arena there are 5 different guns. Probability of hitting aim from gun1 is 0.5.
Probability of hitting aim from gun2 is 0.55. Probability of hitting aim from gun3 is 0.7.
Probability of hitting aim from gun4 is 0.75. Probability of hitting aim from gun5 is 0.4. One shoot was made from a gun selected at random. What is the probability that aim was hit?

Answer & Explanation

Opeance1951

Opeance1951

Beginner2021-11-17Added 26 answers

Step 1
Let us denote A=gun 1, B=gun 2, C=gun 3, D=gun 4, E=gun 5
H=event of hitting
There are total 5 guns. The probability of selecting a gun =15
So, P(A)=P(B)=P(C)=P(D)=P(E)=15
Given that:
The probability of hitting aim from gun 1
=0.5. So, P(HA)=0.5
The probability of hitting aim from gun 2
=0.55. So, P(HB)=0.55
The probability of hitting aim from gun 3
=0.7. So, P(HC)=0.7
The probability of hitting aim from gun 4
=0.75. So, P(HD)=0.75
The probability of hitting aim from gun 5
=0.4. So, P(HE)=0.4
Step 2
The probability that aim was hit is:
P(H)
=P(A and H)+P(B andH)+P(C andH)+P(D andH)+P(E and H)
=P(A)P(HA)+P(B)P(HB)+P(C)P(HC)+P(D)P(HD)+P(E)P(HE)
=(15×0.5)+(15×0.55)+(15×0.7)+(15×0.75)+(15×0.4)
=0.58
Answer: 0.58

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