What you know about your commute:
- Traffic: 30% chance of an accident, 10% chance of construction, 60% chance of no traffic.
- Weather: 70% chance of sun, 30% chance of rain.
- There is a 60% chance it will be sunny and there will be no traffic.
What is the probability that it will be sunny or there will be no traffic? Type your answer as a decimal between 0 and 1 (e.g., 10% = 0.1).
P(sunny or no traffic) = P(sunny) + P(no traffic) − P(sunny and no traffic) = 0.7 + 0.6 − 0.6 = 0.7. Notice the overlap is the entire no-traffic event: whenever there is no traffic, it is sunny.
You added 0.7 + 0.6 but did not subtract the overlap — and no probability can exceed 1! The days that are sunny and traffic-free got counted twice. Subtract P(sunny and no traffic) = 0.6. Try again.
0.6 is P(sunny and no traffic) — the joint probability. The question asks about “or”: P(sunny) + P(no traffic) − P(both). Try again.
It looks like you entered a percent — please answer as a decimal between 0 and 1 (e.g., 40% = 0.4).
Use the addition rule: P(sunny or no traffic) = P(sunny) + P(no traffic) − P(sunny and no traffic). All three pieces are given above. Try again.