Question

1. thomas wants to invite madeline to a party. he has an 80% chance of bumping into her at school. otherwise, he’ll call her on the phone. if he talks to her at school, he’s 90% likely to ask her to a party. however, he’s only 60% likely to ask her over the phone. this is the tree diagram that represents the probability of thomas inviting madeline to a party. tree diagram image what is the total probability of thomas inviting madeline to the party? 84% 64% 90% 100%

Explanation:

Step1: Identify two scenarios

There are two ways Thomas can invite Madeline: bumping into her at school and asking, or calling her and asking.

Step2: Calculate probability for school scenario

Probability of bumping into her at school is \( 0.8 \), and then asking is \( 0.9 \). So the probability for this path is \( 0.8 \times 0.9 = 0.72 \).

Step3: Calculate probability for phone scenario

Probability of not bumping into her (so calling) is \( 1 - 0.8 = 0.2 \), and then asking over phone is \( 0.6 \). So the probability for this path is \( 0.2 \times 0.6 = 0.12 \).

Step4: Sum the probabilities

Total probability is \( 0.72 + 0.12 = 0.84 \), which is \( 84\% \).

Answer:

84%