A supply container dropped from an aircraft by parachute hits a target with a pr

Question

A supply container dropped from an aircraft by parachute hits a target with a probability of 0.37. a. What is the expected number of container drops needed to hit a target? b. If hits from three containers are required to provide sufficient supplies, what is the expected number of containers dropped before sufficient supplies have been provided? c. What is the probability that sufficient supplies are provided by ten container drops? d.) what is the probability that it is the tenth container dropped that completes the provision of supplies?

Explanation / Answer

We have a geometric distribution with p = 0.37 with success defined as hitting the target.
x = number of attempts needed to hit the target.

E(x) = 1/p = 1/.37 = 2.7 (or 3)

Therfore the expected number of container drops needed to hit a target is 3

If hits from three containers are required to provide sufficient supplies , the expected number of containers dropped before sufficient supplies have been provided is 2.7*3 = 8.1

Therefore in 9 attemps sufficient supplies will be provided.

The probability that sufficient supplies are provided by ten container drops is 1.

the probability that it is the tenth container dropped that completes the provision of supplies
tenth trial is a success is (1-0.37)^9 (0.37) = 0.00578

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