Using the binomial distribution, there is a 0.3474 = 34.74% probability of getting one wrong number.
What is the binomial distribution formula?
The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
For this problem, the values of the parameters are given by:
p = 0.15, n = 10.
The probability of getting one wrong number is P(X = 1), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
P(X = 1) = C(10,1) x (0.15)¹ x (0.85)^9 = 0.3474
0.3474 = 34.74% probability of getting one wrong number.
More can be learned about the binomial distribution at https://brainly.com/question/24863377
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