9) recent crime statistics collected over the past year reveal the following fig
ID: 3307278 • Letter: 9
Question
9) recent crime statistics collected over the past year reveal the following figures: 81% of all people arrested were male, 16% of all people arrested were under the age of 18; 7% of all people arrested were female and under the age of 18.
Let MM repesent the event that the person arrested is male, and U18U18 represent the event that the person arrested is under the age of 18.
Part (a) Complete the table below. Use two decimals in each of your answers.
Part (b) A person who was arrested in the past year is randomly chosen. What is the probability that this person is male or under the age of 18? Enter your answer to two decimals.
equation editor
Equation Editor
Part (c) Find the probability that the person chosen in (b) is neither male nor under the age of 18. Use two decimals in your answer.
equation editor
Equation Editor
Part (d) What percentage of all people arrested in the past year are male and at least 18 years of age? Enter your answer as a decimal to two places.
equation editor
Equation Editor
Part (e) Are the events MM and U18U18 mutually exclusive events? Select the most appropriate reason below.
A. MM and U18U18 are mutually exclusive events, because P(MUH)=P(M)P(U18)P(MUH)=P(M)P(U18).
B. MM and U18U18 are not mutually exclusive events, because P(MUH)0P(MUH)0.
C. MM and U18U18 are mutually exclusive events, because P(MUH)=0P(MUH)=0.
D. MM and U18U18 are not mutually exclusive events, because P(MUH)P(M)P(U18)P(MUH)P(M)P(U18).
E. MM and U18U18 are mutually exclusive events, because P(MUH)=0P(MUH)=0
Explanation / Answer
a.
b P(MM or u18u18)=0.81+0.16=0.97 [for two disjoint events, A and B, use addition rule, P(A or B)=P(A)+P(B)]
c. P(MM or u18u18)'=1-P(MM or u18u18)=1-0.97=0.03 [P(A or B)'=1-P(A or B)]
d. P(MM and u18u18)=0.81*0.16=0.13 [for two disjoint events, A and B, use multiplication rule, P(A and B)=P(A)*P(B)]
Therefore, required percentage is:13%.
MM McMc Row probabilities u18u18 0.04 0.12 0.16 u18cu18c 0.77 0.07 0.84 Column probabilities 0.81 0.19 1.00Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.