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Six hunters saw a fox and fired at the same time. Suppose that each of the...

Six hunters saw a fox and fired at the same time. Suppose that each of the hunters can hit the fox in this distance in 1 out of 3 cases. What is the probability that the fox will be hunted down?

Math   Statistics-And-Probability   
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Answer #1

6 hunters saw a fox and fired at the same time.

Suppose that each of the hunters can hit the fox in the given distance, in 1 out of 3 cases.

This means, each hunter has a chance 1/3, of hunting the fox down.

So, the chance that any of these 6 hunters cannot hunt the fox down, is 1-1/3, ie. 2/3.

Now, we have to find the probability that the fox will be hunted down.

This event is complementary to the event that the fox won't be hunted down; which means all 6 hunters miss their shots.

So,

P(The fox will be hunted down)

=1-P(The fox survives)

=1-P(All 6 hunters miss)

So, the probability that the fox will be hunted down, is 0.9122.

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