Question

On average I drive to work 3 days a week, take the bus one day a week and ride my bicycle one day a week. If I drive there is a probability of 0.2 that I will be late. If I take the bus the probability is 0.15 and if I ride it is 0.05 . (a) What is the probability I will be late tomorrow? (b) I was late for work this morning. What is the probability that I drove?

Answer 1

To calculate the probability of being late tomorrow, consider the probabilities for each mode of transportation and their respective probabilities of being late. Then use these probabilities to calculate the overall probability of being late. In this case, the probability of being late tomorrow is 0.131

Step-by-step explanation:

To calculate the probability of being late tomorrow, you need to consider the probabilities for each mode of transportation. Let's assume that you drive, take the bus, or ride your bicycle with equal likelihood. The probability of being late if you drive is 0.2, so the probability of being on time is 0.8. The probability of taking the bus or riding your bicycle and being late is 0.15 and 0.05 respectively.

Using these probabilities, the probability of being late tomorrow can be calculated as follows:

P(Late) = P(Drive) * P(Late | Drive) + P(Bus) * P(Late | Bus) + P(Bicycle) * P(Late | Bicycle)

Substituting the given probabilities:

P(Late) = 0.33 * 0.2 + 0.33 * 0.15 + 0.33 * 0.05 = 0.066 + 0.0495 + 0.0165 = 0.131