Ask Question
14 March, 11:30

Bob can decide to go to work either by car, bus, or commuter train. If he decides to go by car, there is a 50% chance he will be late due to traffic. If he goes by bus, which has special reserved lanes but is sometimes overcrowded, the probability of being late is only 20%. The commuter train, there is a 1% chance that he is late, but is more expensive than the bus. What is the probability that Bob drove to work today given he arrives late to work?

+3
Answers (1)
  1. 14 March, 11:55
    0
    The probability is 0.7043

    Step-by-step explanation:

    Let's call:

    C: Bob goes to work by car

    B: Bob goes to work by bus

    T: Bob goes to work by Train

    L: Bob arrives late to work

    The probability that Bob drove to work today given that he arrives late to work is:

    P (C/L) = P (C∩L) / P (L)

    Where P (L) = P (C∩L) + P (B∩L) + P (T∩L)

    So, the probability P (C∩L) that Bob goes to work by car and arrives late to work is calculate as:

    P (C∩L) = (1/3) * (0.5) = (1/6) = 0.1667

    Because 1/3 is the probability that Bob choose the car and 0.5 is the probability that he will be late at work given that he choose a car.

    At the same way, the probability P (B∩L) that Bob goes to work by bus and arrives late to work and the probability P (T∩L) that Bob goes to work by Train and arrives late to work are calculate as:

    P (B∩L) = (1/3) * (0.2) = (1/15) = 0.0667

    P (T∩L) = (1/3) * (0.01) = (1/300) = 0.0033

    Then P (L) is calculated as:

    P (L) = 0.1667 + 0.0666 + 0.0033

    P (L) = 0.2367

    Finally, The probability P (C/L) that Bob drove to work today given that he arrives late to work is:

    P (C/L) = 0.1667/0.2367 = 0.7043
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Bob can decide to go to work either by car, bus, or commuter train. If he decides to go by car, there is a 50% chance he will be late due ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers