Question

(a) how many outcomes are there? outcome(s) (b) how many outcomes have both linda and bob being chosen? outcome(s) (c) how many outcomes do not have jessica being chosen?

Explanation:

Step1: Count total outcomes

Count all the triplets in the tree - diagram. There are 12 triplets.

Step2: Count outcomes with Linda and Bob

Look for triplets that start with Linda and have Bob as the second - member. There are 3 such triplets: (Linda, Bob, Debra), (Linda, Bob, Jessica), (Linda, Bob, Amanda)

Step3: Count outcomes without Jessica

Exclude all triplets that contain Jessica. There are 6 such triplets: (Linda, Bob, Debra), (Linda, Bob, Amanda), (Linda, John, Debra), (Linda, John, Amanda), (Maria, Bob, Debra), (Maria, Bob, Amanda), (Maria, John, Debra), (Maria, John, Amanda) (wait, no. Let's re - count. Total 12 outcomes. Number of outcomes with Jessica: (Linda, Bob, Jessica), (Linda, John, Jessica), (Maria, Bob, Jessica), (Maria, John, Jessica) → 4. So number of outcomes without Jessica: \(12 - 4=6\))

Answer:

(a) 12
(b) 3
(c) 6