Respuesta :
Answer:
The probability of getting 12 successes out of 15 trials is [tex]P(12) = 0.2501[/tex].
Step-by-step explanation:
Given:
The probability distribution is binomial distribution.
Number of trials are, [tex]n=15[/tex]
Number of successes are, [tex]x=12[/tex]
Probability of success is, [tex]p=0.8[/tex]
Therefore, probability of failure is, [tex]q=1-p=1-0.8=0.2[/tex]
Now, probability of getting 12 successes out of 15 trials is given as:
[tex]P(X=x)=_{x}^{n}\textrm{C}p^{x}q^{n-x}\\P(12)=_{12}^{15}\textrm{C}(0.8)^{12}(0.2)^{15-12}\\P(12)=455\times 0.8^{12}\times 0.2^{3}\\P(12)=0.2501[/tex]
Therefore, the probability of getting 12 successes out of 15 trials is 0.2501.
Applying the binomial distribution, we get that P(X = 12) = 0.2501.
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Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, given by:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, defined by the formula below.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Considering that p is the probability of a success on a single trial.
For this problem, the parameters are [tex]n = 15, p = 0.8[/tex], and we want to find P(X = 12). Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{15,12}.(0.8)^{12}.(0.2)^{3} = 0.2501[/tex]
Thus P(X = 12) = 0.2501.
A similar problem is given at https://brainly.com/question/15557838
