Question

78. 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

The probability that the marksman will hit the target 13 times is 0.279.

Here, we are given that the probability that a marksman will hit a target each time he shoots is 0.89.

Thus, the probability that he will not hit the target = 1 - 0.89 = 0.11

Here, we can use the concept of binomial distribution to find the probability.

There are a total number of 15 trials, thus, n = 15

Success ⇒ marksman hits the target

Probability of success ⇒ p = 0.89

Failure ⇒ marksman fails to hit the target

Probability of failure ⇒ q = 0.11

Number of successful outcomes required ⇒ x = 13

Now, according to the formula for calculating binomial probability-

P(x) = $nCx *p^{x} *q^{n-x}$

P(x) = $15!/(13!*2!) *(0.89)^{13} *(0.11)^{2}$

P(x) = (15*14/2) (0.2198) (0.0121)

P(x) = 105* 0.0026

P(x) = 0.279

Thus, the probability that the marksman will hit the target 13 times is 0.279.

Learn more about probability here-

https://brainly.com/question/25870256

#SPJ4