Question

Suppose the probability of having a car accident is 0.05, and the probability of using a...

Suppose the probability of having a car accident is 0.05, and the probability of using a cellphone while driving is 0.1. Given a driver had a car accident, the probability that he/she was using a cellphone while driving is 0.3. If someone is using a cellphone while driving, what is the probability that he/she would have a car accident? Are these two events (car accident and using cellphone while driving) independent?

Math   Statistics-And-Probability   
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Answer #1

We define following events.

  • denotes the event that a car accident occurs.
  • denotes the event that a cellphone is used while driving.

From the given information,

By definition of conditional probability required probability is given by

Hence, if someone is using a cellphone while driving, 0.15 is the probability that he/she would have a car accident.

Further, we observe as follows.

Hence, we can conclude that these two events (car accident and using cellphone while driving) are dependent.

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