First, let's understand the situation. This town in New Zealand is very windy. The wind speed each day can be anywhere from 20 to 45 km/hr, and it's equally likely to be any speed in that range. If the wind speed is predicted to be more than 30.4 km/hr, they announce a weather warning on the news. The wind speed each day doesn't depend on the wind speed on any other day.

We want to find out the chance that, over the next 5 days, there will be a weather warning on fewer than 3 of those days.

First, we need to find the probability of a weather warning being issued on any given day. This happens when the wind speed is more than 30.4 km/hr. Since the wind speed is equally likely to be anywhere from 20 to 45 km/hr, the chance of this happening is (45 - 30.4) / (45 - 20) = 0.58 (or 58%).

Now, we want to find the probability of having a weather warning on 0, 1, or 2 days out of the next 5 days.

For 0 days, this means that all 5 days have wind speeds of 30.4 km/hr or less. The chance of this happening on any given day is (1 - 0.58) = 0.42 (or 42%). Since the wind speeds each day are independent, we can just multiply the probabilities for each day together, so the chance of this happening is (0.42)^5 = 0.01 (or 1%).

For 1 day, this means that one day has a wind speed of more than 30.4 km/hr and the other four days have wind speeds of 30.4 km/hr or less. There are 5 different ways this could happen (the windy day could be any one of the 5 days), so the chance of this happening is 5 * (0.58) * (0.42)^4 = 0.15 (or 15%).

For 2 days, this means that two days have wind speeds of more than 30.4 km/hr and the other three days have wind speeds of 30.4 km/hr or less. There are (5 choose 2) = 10 different ways this could happen, so the chance of this happening is 10 * (0.58)^2 * (0.42)^3 = 0.32 (or 32%).

So, the total probability of having a weather warning on fewer than 3 of the next 5 days is 0.01 + 0.15 + 0.32 = 0.48 (or 48%).

Question

First, let's understand the situation. This town in New Zealand is very windy. The wind speed each day can be anywhere from 20 to 45 km/hr, and it's equally likely to be any speed in that range. If the wind speed is predicted to be more than 30.4 km/hr, they announce a weather warning on the news. The wind speed each day doesn't depend on the wind speed on any other day.

We want to find out the chance that, over the next 5 days, there will be a weather warning on fewer than 3 of those days.

First, we need to find the probability of a weather warning being issued on any given day. This happens when the wind speed is more than 30.4 km/hr. Since the wind speed is equally likely to be anywhere from 20 to 45 km/hr, the chance of this happening is (45 - 30.4) / (45 - 20) = 0.58 (or 58%).

Now, we want to find the probability of having a weather warning on 0, 1, or 2 days out of the next 5 days.

For 0 days, this means that all 5 days have wind speeds of 30.4 km/hr or less. The chance of this happening on any given day is (1 - 0.58) = 0.42 (or 42%). Since the wind speeds each day are independent, we can just multiply the probabilities for each day together, so the chance of this happening is (0.42)^5 = 0.01 (or 1%).

For 1 day, this means that one day has a wind speed of more than 30.4 km/hr and the other four days have wind speeds of 30.4 km/hr or less. There are 5 different ways this could happen (the windy day could be any one of the 5 days), so the chance of this happening is 5 * (0.58) * (0.42)^4 = 0.15 (or 15%).

For 2 days, this means that two days have wind speeds of more than 30.4 km/hr and the other three days have wind speeds of 30.4 km/hr or less. There are (5 choose 2) = 10 different ways this could happen, so the chance of this happening is 10 * (0.58)^2 * (0.42)^3 = 0.32 (or 32%).

So, the total probability of having a weather warning on fewer than 3 of the next 5 days is 0.01 + 0.15 + 0.32 = 0.48 (or 48%).

Knowee AI · Accepted Answer