Question

PROBLEM A Suppose a study of speeding violations and drivers who use cell phones produced the following data: Speeding Violation last year No Speeding Violation last year Used cell phone as driver Did not use cell phone as a driver 280 25 405 45 Total 70 685 Referring to Problem A, , if a random person is selected from this sample, what is the probability that the person used a cell phone as a driver? a) 81.9% b) 90.7% c) 40.4% d) 8.2% 1. 2. Referring to Problem A, given that the randomly selected person used a cell phone as a driver, wha is the probability that he/she got a Speeding Violation last year? a) 81.9% b) 90.7% c) 40.4% d) 8.2% 3. Referring to Problem A, , if P(A) = Speeding Violation last year, then P(A)= a) 81.9% b) 90.7% c) 40.4% d) 8.2% 4. Referring to Problem A what is the probability that a randomly selected person did not use a phone as a driver or had no Speeding Violation last year? a) 730 b) 0.967 c) 1.503 d) 11.35

Answer 1

According to the question given,

1) Probability of a person using cell phone as a driver= (Total people using cell phone as a driver)/( Total number of people)

=305/755 = 0.4039 = 40.4 % ( Option C)

2) Probability of a person getting speeding violation = (Total people with speeding violation last year)/ (Total people using cell phone as a driver)

= 25/305 = 0.0819 = 8.2% ( Option D)

3) P(A)= Speeding violation last year= (Total people with speeding violation)/ (Total number of people)

= 70/755 = 0.0927 =9.27%

Therefore, P(A^c)= 100%- 9.27% = 90.73% = 90.7% (Option B)

4) Probability that a randomly selected person did not use phone as a driver = (Probability of not using a cell phone as driver)/ (Total number of people)

= 450/755 =0.596

Probability that a randomly selected person had no speeding violations last year= (People with no speeding violation last year)/ (Total People)

= 685/755 = 0.907

Now, Probability that a randomly selected person did not use phone as a driver or had no speeding violations last year= Probability that a randomly selected person did not use phone as a driver + Probability that a randomly selected person had no speeding violations last year

=0.596+0.907 = 1.503 (Option C)