You check the weather before you begin your drive and see that it is raining and will continue to rain all day.
Given that it is rainy, what is the probability that there will be an accident on your commute? Use the table below.
| Rainy | Sunny | Total |
|---|
| Accident | 25% | 5% | 30% |
|---|
| Construction | 5% | 5% | 10% |
|---|
| No traffic | 0% | 60% | 60% |
|---|
| Total | 30% | 70% | 100% |
|---|
Type your answer as a decimal between 0 and 1, rounded to two decimal places (e.g., 10% = 0.1).
P(accident | rainy) = P(accident and rainy) / P(rainy) = 0.25 / 0.30 ≈ 0.83. Knowing it is rainy shrinks your world to the Rainy column — the 25% joint probability gets rescaled by the 30% chance of rain.
0.25 is P(accident and rainy) — the joint probability, before you knew the weather. But you know it is raining, so rescale by the Rainy column total: 0.25 / 0.30. Try again.
0.3 is the overall P(accident), ignoring the weather — but you have information: it is raining. Condition on the Rainy column: P(accident and rainy) / P(rainy). Try again.
It looks like you multiplied 0.25 × 0.30 — but conditional probability divides the joint probability by the marginal: P(accident and rainy) / P(rainy). Try again.
It looks like you entered a percent — please answer as a decimal between 0 and 1 (e.g., 40% = 0.4).
Given rain, you live in the Rainy column of the table. P(accident | rainy) = P(accident and rainy) / P(rainy) = 0.25 / 0.30. Try again.