Question

The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.

Answer 1

A shooter has a 27.92% chance of hitting the target at least 13 times.

What does binomial distribution mean?

• Let X become a random variable and represent the number of times the target gets hit.
• 15 shots are fired, hence 10 trials ("n") are conducted as a result.
• The likelihood of success is represented by "p" in a binomial distribution, and the likelihood of failure is represented by "q" (where q = 1 - p).
• p = 0.89 with q = 0.11 because the target has a 0.89 chance of being hit.

This probability mass function in this type of binomial distribution is the quantity of successes ("x").

P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ

The required number of wins is five since we are concerned with the likelihood that target will be hit exactly five times.(i.e., x = 13).

P(X = 13) =  ¹⁵C₁₃. (0.89)¹³ (0.11)²

P(X = 13) = 0.2792

P(X = 13) = 27.92%

Therefore, there is a 27.92% chance that a shooter will hit its target at the very most 13 times.

To know more about the binomial distribution, here

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