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int) A group of 10 hunters wait for ducks to fly by. When a flock of ducks flies overhead, the hunters all fire at the same time, each selecting a target at random and independently of the others. If each hunter independently hits his target with probability 0.4, and if all misses do not hit other ducks, what is the expected number of ducks that will be hit

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Answer:

The expected number of ducks that will be hit is 4.

Step-by-step explanation:

For each hunter, there are only two possible outcomes. Either they hit a duck, or they do not. The probability of a hunter hitting a ducks is independent of any other hunter. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

A group of 10 hunters wait for ducks to fly by.

This means that [tex]n = 10[/tex]

Each hunter independently hits his target with probability 0.4

This means that [tex]p = 0.4[/tex]

What is the expected number of ducks that will be hit?

[tex]E(X) = np = 10*0.4 = 4[/tex]

The expected number of ducks that will be hit is 4.

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