Question

Answer the following questions by referring to the accompanying table, which lists the highway patrol’s reasons for stopping cars and the number of tickets issued.

Reasons for stopping car	Issued ticket	Did not issue ticket	Total
Speeding	40	170	210
No taillights	10	35	45
Failure to use signals	5	25	30
Careless driving	45	70	115
TOTAL	100	300	400

Assume that a car was stopped.

1. What is the probability that a ticket was issued?
2. What is the probability that the car did not have taillights?
3. What is the probability that a driver will get a ticket, given that he or she was stopped for careless driving?
4. What is the probability that the person was stopped for speeding or for failure to use signals?
5. Given that a ticket was not issued, what is the probability that the person was stopped for speeding?

Answer 1

(A) total number of ticket = 400 and total number of issued ticket = 100

So, probability = (number of issue ticket)/(total tickets)

= 100/400

= 0.25

(B) total number of ticket = 400 and total number of car that did not have taillights = 45

So, probability = (number of car that did not have taillights )/(total tickets)

= 45/400

= 0.1125

(C) total number of cars stopped for careless driving = 115 and number of issued ticket for careless driving and gets ticket = 45

So, probability = (number of issued ticket for careless driving)/(total number of cars stopped for careless driving)

= 45/115

= 0.3913

(D) total number of ticket = 400 and total number of cars stopped for speeding or for failure to use signals = 210+30 = 240

So, probability = (total number of cars stopped for speeding or for failure to use signals)/(total tickets)

= 240/400

= 0.6000

(E) number of person who were stopped for speeding and ticket was not issued= 170 and total number of not issue ticket = 300

so,probability = (number of person who were stopped for speeding and ticket was not issued)/(total number of not issue ticket)

= 170/300

= 0.5667