Answer:
0.624
Step-by-step explanation:
Given that:
Number of copiers with the company = 4
It is a binomial experiment.
Probability that on a given day, one copier will break down = [tex]\frac{23}{50}[/tex]
[tex]p = \frac{23}{50}[/tex] = 0.46
[tex]q = 1-p = 1-\frac{23}{50}= \frac{27}{50}[/tex] = 0.54
Formula for Binomial probability:
[tex]P(x=r) = _{n}C_{r}p^rq^{n-r}[/tex]
We have to find [tex]P(x >= 2)[/tex]
[tex]P(x >= 2) = P(X=2)+P(X=3)+P(X=4)[/tex]
[tex]P(x=2) = _{4}C_{2}0.46^2\times 0.54^{2} = 0.37\\P(x=3) = _{4}C_{3}0.46^3\times 0.54 = 0.21\\P(x=4) = _{4}C_{4}0.46^4\times 0.54^{0} = 0.044[/tex]
[tex]P(x >= 2) = 0.37 + 0.21 + 0.044 = \bold{0.624}[/tex]
Following are the calculation to the given binomial experiment:
Given:
Please find the given question.
To find:
probability =?
Solution:
Let the probability of one copy is broken down then [tex]\bold{(p) =\frac{2}{5}}\\[/tex]
[tex]\to q=1-p\\\\[/tex]
[tex]=1-\frac{2}{5}\\\\=\frac{5-2}{5}\\\\=\frac{3}{5}\\\\[/tex]
Using the binomial distribution:
[tex]P(X = x) = ^n C_r \times p \times q^{n-x}[/tex]
Calculating the probability in which the copy of 2 will break down on a given day:
[tex]P(X=2)=^4 c_2 \times (\frac{2}{5})^2\times (\frac{3}{5})^{4-2}[/tex]
[tex]= \frac{4!}{4-2! \times 2!}\times (\frac{2}{5})^2\times (\frac{3}{5})^{2}\\\\= \frac{4\times 3 \times 2!}{2! \times 2\times 1}\times (\frac{4}{25})\times (\frac{9}{25})\\\\= \frac{12}{ 2}\times (\frac{4}{25})\times (\frac{9}{25})\\\\=4\times (\frac{4}{25})\times (\frac{9}{25})\\\\=\frac{144}{625}\\\\=0.2304[/tex]
Therefore, the final answer is "0.2304".
Learn more:
brainly.com/question/14085738
