Probability algebra 2 question?

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

Maximus VonRueden · Accepted Answer

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 = 0.018Add these together:0.03 + 0.018= 0.048Answer: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 distracted0.018 –> accident happened while not distractedWe want the first case (accident while distracted) compared to the total probability of any accident (two cases added together).So basically it is:0.030.03 + 0.018We already figured out the denominator from part A: 0.030.048That reduces to:30 .. 5— = — = 0.62548 .. 8Answer:62.5% a driver that was in an accident was distracted

Maximus VonRueden · Answer

Hope you understand better.

Oran Armstrong

Probability algebra 2 question?

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