To calculate the probability a driver will be in an accident, we can use the Law of Total Probability. Let A be the event that a driver is in an accident, and D be the event that a driver is distracted.
P(A) = P(A|D) * P(D) + P(A|D') * P(D')
P(A) = 0.30 * 0.10 + 0.02 * 0.90
P(A) = 0.03 + 0.018
P(A) = 0.048
Therefore, the probability that a driver will be in an accident is 4.8%. This means that out of all drivers, there is a 4.8% chance that they will be in an accident.
To calculate the probability that a driver who was in an accident was distracted, we can use Bayes' Theorem. Let B be the event that a driver was distracted given they were in an accident.
P(D|A) = P(A|D) * P(D) / P(A)
P(D|A) = 0.30 * 0.10 / 0.048
P(D|A) = 0.03 / 0.048
P(D|A) = 0.625
Therefore, the probability that a driver who was in an accident was distracted is 62.5%. This means that out of all drivers who were in an accident, there is a 62.5% chance that they were distracted.
provided.
The police department is keeping track of distracted drivers and accidents. They have found that if a driver is distracted, the driver has a 30% chance of being in an accident. If the driver is not distracted, the driver has a 2% chance of being in an accident. The probability of a driver being distracted is 10%. If needed, create a tree diagram on a separate piece of paper. Then use the diagram to answer the questions.
What is the probability a driver will be in an accident? Explain.
What is the probability that a driver who was in an accident was distracted? Explain.
(2 points)
1 answer