Question

a class is choosing a president and a vice president.
there are three students running for president: linda, ann, and maria.
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
linda
├─ john (linda, john)
├─ jim (linda, jim)
└─ bob (linda, bob)
ann
├─ john (ann, john)
├─ jim (ann, jim)
└─ bob (ann, bob)
maria
├─ john (maria, john)
├─ jim (maria, jim)
└─ bob (maria, 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 have linda or maria being chosen?
□ outcome(s)

Explanation:

Part (a)

Step1: Count outcomes per president

For each president (Linda, Ann, Maria), there are 3 vice - president options.

Step2: Calculate total outcomes

Since there are 3 presidents and 3 vice - presidents, total outcomes = \(3\times3 = 9\). Also, by directly counting from the tree diagram: Linda has 3, Ann has 3, Maria has 3. So \(3 + 3+3=9\).

Step1: Identify the relevant outcome

We are looking for outcomes where Ann is president and Jim is vice - president. From the tree diagram, the outcome is (Ann, Jim).

Step2: Count the number of such outcomes

There is only 1 such outcome.

Step1: Count outcomes for Linda

Linda has 3 outcomes: (Linda, John), (Linda, Jim), (Linda, Bob).

Step2: Count outcomes for Maria

Maria has 3 outcomes: (Maria, John), (Maria, Jim), (Maria, Bob).

Step3: Calculate total outcomes for Linda or Maria

To find the number of outcomes with Linda or Maria, we add the number of outcomes for Linda and Maria. So \(3 + 3=6\).

Answer:

9

Part (b)