Question

) In New South Wales, each adult on the electoral roll has a 10% of being called up for jury duty in any year. A company has 25 employees on the electoral roll. i) What is the probability that more than two employees are called up for jury duty in any year

Answer 1

The probability is
`0.4629`

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 :

`p=0.1`

We also know that a company has 25 employees on the electoral roll.

We can write this as :

`n=25`

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
`(p=0.1)`

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
`n=25` (being this number the total employees of the company).

We define the random variable as :

`X :` '' Number of employees being called up for jury duty in any year from the total of 25 employees ''

⇒
`X` ~ Bi ( n , p ) ⇒
`X` ~ Bi ( 25 , 0.1 )

This means that
`X` can be modeled as a Binomial random variable with parameters ''n'' and ''p''.

We can calculate probabilities using the following equation :

`P(X=x)=(nCx)p^(x)(1-p)^(n-x)`

Where
`nCx` is the combinatorial number define as :

`nCx=(n!)/(x!(n-x)!)`

We want to calculate
`P(X>2)` ⇒

`P(X>2)=1-P(X\leq 2)` ⇒

`P(X>2)=1-[P(X=0)+P(X=1)+P(X=2)]`

`P(X>2)=0.4629`

We found out that the probability is
`0.4629`