Question: A air defense system has an effectiveness value to kill a single incoming target by firing one missile of 0.75. Assume targets and kills are

A air defense system has an effectiveness value to kill a single incoming target by firing one missile of 0.75. Assume targets and kills are independent events.

(a) What is the probability of killing an incoming target by shooting two missiles at it?

(b) What are the probabilities killing an incoming target by shooting 3, 4, and 5 missiles at it?

(c) How many missiles should be fired to kill an incoming target with a probability of 0.99?

(d) How many missiles should be fired to kill a two incoming targets with a probability of 0.99 each? Construct a plot that shows the number of missiles needed to kill n incoming targets with a probability of 0.99 each as a function of n.

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