Question

Adam, Jack and Sheila have been elected to the Board of Directors for a community organization. The president and vice president are randomly selected from these people by drawing their names from a hat. What is the probability that Jack will be selected first for president and Sheila will be selected second for vice president?

Answer 1

The probability is 1/6.

There is a 1/3 chance he will be elected president. After his name is drawn, there are only 2 remaining; this makes the probability she is vice-president 1/2. Together we have

(1/3)(1/2) = 1/6

Answer 2

Answer:
`(1)/(6)`

Explanation:

Given: The number of persons elected to the Board of Directors for a community organization = 3

To select person first for president and then for president, the total number of ways =
`^3P_2=(3!)/((3-2)!)=(3!)/(1!)=6`

The number of ways Jack will be selected first for president and Sheila will be selected second for vice president = 1

Then , the probability that Jack will be selected first for president and Sheila will be selected second for vice president is given by :-

`P=\frac{\text{Favorable}}{\text{Total}}=(1)/(6)`