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The probability of a man hitting the target at a shooting range is \(\frac{1}{4}\). If he shoots 10 times, what is the probability that he hits the target exactly three times?

Answer :

Final answer:

The probability of the man hitting the target exactly 3 times out of 10 attempts is approximately 25.03%, calculated using the Binomial Probability Formula.

Explanation:

To determine the probability of a particular outcome in a series of events like this, we can use the Binomial Probability Formula which is P(k; n, p) = C(n, k) * (p^k) * ((1-p)^(n-k)) where k is the number of successful trials (hits), n is the total number of trials (shots), and p is the probability of a successful trial (hitting the target). Here, the man hits the target 3 times out of 10 attempts, with the probability of success on each trial being 1/4.

So, plugging these values into the formula we get: P(3; 10, 1/4) = C(10, 3) * ((1/4)^3) * ((1-1/4)^(10-3)) = (10! / (3!(10-3)!))*(1/64)*((3/4)^7).
From calculations, we get the answer as approximately 0.2503 or 25.03%.

Learn more about Binomial Probability here:

https://brainly.com/question/33993983

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