An army officer plans to hit a target with five independent and identical missil

Question

An army officer plans to hit a target with five independent and identical missiles. The chance that a missile can hit a target is: 0.9714285 find the probability that:

a. None of the missile will hit the target.

b. one missiles will hit the target.

c. Two missiles will hit the target.

d. three missiles will hit the target.

e. four missiles will hit the target.

f. all the five missiles will hit the target.

g. At least three missiles will hit the target.

h. at the most three missiles will hit the target.

i. find the average number of hits.

j. find the variance of the number of hits

2. police station records show that among females who were kidnapped 80% were kidnapped out of greed and 20% were kidnapped due to love affairs. There is 14% chance that a female kidnapped out of greed will be killed by the kidnapper and there is 7% chance taht a female kidnapped due to a love affair will be killed by the kidnapper. Mis kitty was kidnapped and killed. (a). what is the conditional probability that miss kitty was killed due to a love affair? (b). What is the conditional probability that miss kitty was killed out of greed?

Explanation / Answer

1) the probability that the missile will hit the target = 0.9714285

therefore probability that missile will miss the target = 1- 0.9714285 = 0.0285715

n = 5

A)p(x= 0) =  0.0285715^5 = 0.00000002

B)P(X=1) = 5C1*(0.9714285)^1*(0.0285715)^4

= 0.000003

C) P(X=2) = 5C2*(0.9714285)^2*(0.0285715)^3 = 0.00022

D) P(X=3) = 5C3*(0.9714285)^3*(0.0285715)^2 = 0.0074

E) = P(X=4) = 5C4*(0.9714285)^4*(0.0285715)^1 = 0.1272  

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