While on a camping trip, Walter is thinking about riding his bike to one of the two hills. There are some chances of rain and it is possible that the roads to the hills are blocked after the recent storm. Walter is willing to attempt a ride to a hill if the probability of avoiding both rain and a blocked road is higher than 50%. Based on the probabilities in the table, what are Walter’s options?

Question

While on a camping trip, Walter is thinking about riding his bike to one of the two hills. There are some chances of rain and it is possible that the roads to the hills are blocked after the recent storm. Walter is willing to attempt a ride to a hill if the probability of avoiding both rain and a blocked road is higher than 50%. Based on the probabilities in the table, what are Walter’s options?

Answer 1

To determine Walter's options, we need to calculate the probability of avoiding both rain and a blocked road for each hill. We will use the probabilities provided in the table.

For Hill 1:
Probability of avoiding rain = 1 - Probability of rain = 1 - 0.25 = 0.75
Probability of avoiding a blocked road = 1 - Probability of road block = 1 - 0.2 = 0.8
Probability of avoiding both rain and a blocked road = Probability of avoiding rain × Probability of avoiding a blocked road = 0.75 × 0.8 = 0.6

For Hill 2:
Probability of avoiding rain = 1 - Probability of rain = 1 - 0.15 = 0.85
Probability of avoiding a blocked road = 1 - Probability of road block = 1 - 0.4 = 0.6
Probability of avoiding both rain and a blocked road = Probability of avoiding rain × Probability of avoiding a blocked road = 0.85 × 0.6 = 0.51

Based on these calculations, we can see that the probability of avoiding both rain and a blocked road is higher than 50% for Hill 1 (0.6) but not for Hill 2 (0.51). Therefore, Walter's option is:

A. Hill 1 only

Answer 2

To determine Walter's options, we need to calculate the probability of avoiding both rain and a blocked road for each hill.

For Hill 1, the probability of avoiding rain is 1 - 0.25 = 0.75, and the probability of avoiding a blocked road is 1 - 0.2 = 0.8. The probability of avoiding both rain and a blocked road for Hill 1 is 0.75 * 0.8 = 0.6.

For Hill 2, the probability of avoiding rain is 1 - 0.15 = 0.85, and the probability of avoiding a blocked road is 1 - 0.4 = 0.6. The probability of avoiding both rain and a blocked road for Hill 2 is 0.85 * 0.6 = 0.51.

Since the probability of avoiding both rain and a blocked road is higher for Hill 1 (0.6) than Hill 2 (0.51), Walter's best option is to attempt a ride to Hill 1 only.

Therefore, the correct answer is A. Hill 1 only.