We are interested in analyzing data related to car accidents, age, and gender. U

Question

We are interested in analyzing data related to car accidents, age, and gender. Use U to denote under 21 years old and M to denote Male. The probability that someone gets in a car accident and is under 21 years old is 21%. The probability that someone gets in a car accident and is male is 67%. The probability that they get in a car accident and are a male under the age of 21 is 14%. a. b. c. d. e. f. g. What percentage of people get in a car accident and are under the age of 21 or male? What percentage of people get in a car accident and are not male? Given someone is under the age of 21, what is the probability they are also male? What percentage of people get in a car accident and are not under the age of 21 nor male? Are U and M mutually exclusive events? Why or why not? Are U and M independent events? Explain, using probabilities If we know someone is Male, what is the probability they are also under the age of21?

Explanation / Answer

Ans:

P(U)=0.21

P(M)=0.67

P(U and M)=0.14

a)P(U or M)=P(U)+P(M)-P(U and M)

=0.21+0.67-0.14

=0.74

b)P(not M)=1-0.67=0.33

c)P(M/U)=P(U and M)/P(U)=0.14/0.21=0.67

d)P(U or M)'=1-P(U or M)=1-0.74=0.26

e)U and M are not mutually exclusive,as P(U and M) is not equal to 0.

f)P(U and M)=0.14

P(U)*P(M)=0.21*0.67=0.14

As,P(U and M)=P(U)*P(M)=0.14,so U and M are independent events.

g)P(U/M)=P(U and M)/P(M)=0.14/0.67=0.21

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