2. An insurance company surveyed 150 drivers. The survey showed that 115 drivers had no accident for at least one year, 46 had at least one traffic violation this past year, and 21 drivers surveyed had at least one violation and an accident this past year. Answer the following questions. Drawing a Venn diagram may be help.

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Can you answer question 2?? Please and thank you.

2. An insurance company surveyed 150 drivers. The survey showed that 115 drivers had
no accident for at least one year, 46 had at least one traffic violation this past year, and
21 drivers surveyed had at least one violation and an accident this past year. Answer the
following questions. Drawing a Venn diagram may be help.
(a) If a driver is selected at random, what is the probability that the selected driver had no
violation and no accident this past year?
(b) If a driver is selected at random, what is the probability that he/she had no traffic
violation this past year but had an accident?
E
F
ENF
Transcribed Image Text:2. An insurance company surveyed 150 drivers. The survey showed that 115 drivers had no accident for at least one year, 46 had at least one traffic violation this past year, and 21 drivers surveyed had at least one violation and an accident this past year. Answer the following questions. Drawing a Venn diagram may be help. (a) If a driver is selected at random, what is the probability that the selected driver had no violation and no accident this past year? (b) If a driver is selected at random, what is the probability that he/she had no traffic violation this past year but had an accident? E F ENF
Expert Solution
Step 1

Given data:

The total numbers of drivers are n(U)=150.

The number of drivers that had no accidents is n(S)=115.

The numbers of drivers that had at least one traffic violation are n(V)=46.

The numbers of drivers that have one violation and accident in the past year are n(A)=21.

(a)

The expression for the probability that the selected driver had no accident and no violation in the past year is,

PX=nS-nV-nAnS

Substitute the given values in the above expression.

PX=115-46-21150=90150=0.6

 

Thus, the probability that the selected driver had no accident and no violation in the past year is 0.6.

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