An elementary school bus comes at 8:15 am every morning to pick up children in a neighborhood. The probability that the bus will be late is 0.19 and the probability that the bus will be early is 0.02.
What is the probability that the bus will arrive early next two days?
What is the probability that the bus will arrive on time next two days?
In two or more complete sentences, explain your calculations for parts A and B. In your explanation, include their similarities and differences.
To calculate the probability that the bus will arrive early next two days, we multiply the probability of the bus being early on the first day (0.02) by the probability of it being early on the second day. Since the events are independent, we simply multiply the probabilities together. So the probability of the bus arriving early on both days is 0.02 * 0.02 = 0.0004.
To calculate the probability that the bus will arrive on time next two days, we need to consider all possible combinations of the bus being early, on time, or late on each day. There are 3 possibilities: early-early, on time-on time, and late-late. The probabilities for each of these combinations are: (0.02 * 0.02) + ((1 - 0.19) * (1 - 0.19)) + (0.19 * 0.19) = 0.0004 + 0.5929 + 0.0361 = 0.6294.
The calculations for both parts involve multiplying probabilities together. The difference is that for part A, we multiply the probability of the bus being early on the first day with the probability of it being early on the second day. For part B, we consider all possible combinations of events and calculate the total probabilities for each combination.