Question

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. What is the probability of Thomas inviting Madeline to the party at school?

Answer 1

84%

Explanation:

The probability of Thomas bumping into her at school is 80%, so the probability of not bumping into her is 100% - 80% = 20%.

If he doesn't bump into her (20% chance), he will call her, and the probability of asking her in this case is 60%, so the final probability of asking her in this case is:

`P_1 = 20\% * 60\% = 12\%`

If he bumps into her (80% chance), the probability of asking her is 90%, so the final probability of asking her in this case is:

`P_2 = 80\% * 90\% = 72\%`

To find the probability of Thomas inviting Madeline to the party, we just have to sum the probabilities we found above:

`P = P_1 + P_2`

`P = 12\% + 72\% = 84\%`