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

Answer: $\dfrac{1}{6}$

Step-by-step 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 = $^3P_2=\dfrac{3!}{(3-2)!}=\dfrac{3!}{1!}=6$

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 :-

$P=\dfrac{\text{Favorable}}{\text{Total}}=\dfrac{1}{6}$

Answer 2

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