Question

a class is choosing a president and a vice president.
there are four students running for president: ann, maria, jessica, and linda.
there are three students running for vice president: john, jim, and bob.
the tree diagram below shows the possible outcomes. use the diagram to answer the questions.
president vice president outcome
ann
john (ann, john)
jim (ann, jim)
bob (ann, bob)
maria
john (maria, john)
jim (maria, jim)
bob (maria, bob)
jessica
john (jessica, john)
jim (jessica, jim)
bob (jessica, bob)
linda
john (linda, john)
jim (linda, jim)
bob (linda, bob)
(a) how many outcomes are there?
□ outcome(s)
(b) how many outcomes have both ann and jim being chosen?
□ outcome(s)
(c) how many outcomes do not have linda being chosen?
□ outcome(s)

Explanation:

Step1: Count total outcomes

For each of the 4 president candidates, there are 3 vice - president candidates. Using the multiplication principle \(4\times3 = 12\).

Step2: Find outcome with Ann and Jim

Looking at the tree diagram, the outcome \((Ann,Jim)\) is 1.

Step3: Count outcomes without Linda

There are 3 president candidates (Ann, Maria, Jessica) and 3 vice - president candidates. Using the multiplication principle \(3\times3=9\).

Answer:

(a) \(12\)
(b) \(1\)
(c) \(9\)