Probability algebra 2 question?

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.

a. What is the probability a driver will be in an accident? Explain.

b. What is the probability that a driver who was in an accident was distracted? Explain

Can anyone walk me step by step through this? I’m really having trouble with this unit and would really appreciate it!

2 Answers

  • First draw a probability tree. Start with branches for distracted and not distracted. Then branch off of there for accident or no accident. Be sure to include the percentages for each branch, as a decimal:

    …………… …………. / Accident (0.30)

    ../ Distracted (0.10)

    ./ …………. …………. No accident (0.70)

    /

    . …………… …………… / Accident (0.02)

    .. Not distracted (0.90)

    ………………. …………… No accident (0.98)

    PART A:

    There are two cases.

    Driver was distracted (0.10) and had an accident (0.30)

    0.10 x 0.30 = 0.03

    Driver was not distracted (0.90) and had an accident (0.02)

    0.90 x 0.02 = 0.018

    Add these together:

    0.03 + 0.018

    = 0.048

    Answer:

    4.8%

    PART B:

    This is a little trickier. Here we can ignore the cases where the driver did not have an accident. We have only two cases, as we figured out in part A.

    0.03 –> accident happened while distracted

    0.018 –> accident happened while not distracted

    We want the first case (accident while distracted) compared to the total probability of any accident (two cases added together).

    So basically it is:

    0.03


    0.03 + 0.018

    We already figured out the denominator from part A:

    0.03


    0.048

    That reduces to:

    30 .. 5

    — = — = 0.625

    48 .. 8

    Answer:

    62.5% a driver that was in an accident was distracted

  • Hope you understand better.

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