Question

8) A committee has fifteen members. There are two members that currently serve as the board’s chairman and vice chairman. Each member is equally likely to serve in any of the positions. Two members are randomly selected and assigned to be the new chairman and vice chairman. What is the probability of randomly selecting the two members who currently hold the positions of chairman and vice chairman and assigning them to their current positions

Answer 1

The probability is
`P(Z) = 0.0064`

Explanation:

From the question we are told that

The number of members is n = 15

Generally the number of ways of selecting two member from the fifteen members is mathematically represented as

`K  =  ^(n)C_2 *  2!`

Here C stands for combination hence we will be making use of the combination functionality in our calculator

`K  =  ^(15)C_2 *  2 * 1`

=>
`K  =  78  *  2 * 1`

=>
`K  =  156`

Gnerally the number of outcome that matches the outcome required by the committee(Which is reselecting the member who where the chairman and vice chairman of the board ) is m = 1

Generally the probability of randomly selecting the two members who currently hold the positions of chairman and vice chairman and assigning them to their current positions is mathematically represented as

`P(Z) =  (m)/(K)`

=>
`P(Z) =  (1)/(156)`

=>
`P(Z) =  (1)/(156)`

=>
`P(Z) = 0.0064`