Answer:
The probability is [tex]0.4629[/tex]
Step-by-step explanation:
We know that in New South Wales, each adult on the electoral roll has a 10 % of being called up for jury duty in any year.
We can write this probability as :
[tex]p=0.1[/tex]
We also know that a company has 25 employees on the electoral roll.
We can write this as :
[tex]n=25[/tex]
Now we can assume that this is a Bernoulli process in which the election of a random adult is independent and also the probability of being called remains the same [tex](p=0.1)[/tex]
We also define the Binomial random variable in the Bernoulli process that counts the number of successes given that we set a number of individual experiments.
In this exercise, we will call a ''success'' when an adult is being called up for jury duty. We also set the number of experiments to [tex]n=25[/tex] (being this number the total employees of the company).
We define the random variable as :
[tex]X :[/tex] '' Number of employees being called up for jury duty in any year from the total of 25 employees ''
⇒ [tex]X[/tex] ~ Bi ( n , p ) ⇒ [tex]X[/tex] ~ Bi ( 25 , 0.1 )
This means that [tex]X[/tex] can be modeled as a Binomial random variable with parameters ''n'' and ''p''.
We can calculate probabilities using the following equation :
[tex]P(X=x)=(nCx)p^{x}(1-p)^{n-x}[/tex]
Where [tex]nCx[/tex] is the combinatorial number define as :
[tex]nCx=\frac{n!}{x!(n-x)!}[/tex]
We want to calculate [tex]P(X>2)[/tex] ⇒
[tex]P(X>2)=1-P(X\leq 2)[/tex] ⇒
[tex]P(X>2)=1-[P(X=0)+P(X=1)+P(X=2)][/tex]
[tex]P(X>2)=0.4629[/tex]
We found out that the probability is [tex]0.4629[/tex]
