Final answer:
The total probability that Soren makes it to class on time is 0.72, calculated by adding 0.24 (the result of 0.40 × 0.60 for hitting snooze) and 0.48 (the result of 0.60 × 0.80 for not hitting snooze). The options provided in the question don't match this answer, suggesting an issue with the question or provided options.
Step-by-step explanation:
To calculate the probability that Soren makes it to class on time, we need to consider both scenarios separately and then add the probabilities together. The first scenario is when Soren hits the snooze button, which happens with a probability of 0.40, and in this case he still has a 0.60 probability of making it on time. The second scenario is when he does not hit snooze, which has a probability of 0.60 (1 - the probability of hitting the snooze), and in this case he has a 0.80 probability of being on time.
To find the overall probability of Soren being on time, we calculate:
(Probability of snooze) × (Probability of being on time given snooze) + (Probability of no snooze) × (Probability of being on time given no snooze)
- 0.40 × 0.60 = 0.24
- 0.60 × 0.80 = 0.48
Add these two scenarios together to get the total probability that Soren makes it to class on time:
0.24 + 0.48 = 0.72
Therefore, the probability that Soren makes it to class on time is 0.72, which was not one of the provided options. There seems to be a mistake since option D, 0.64, is the closest but is not the correct answer based on the given probabilities.