Question

Exercise 1: probability Concepts

Part one: Contingency table and Probability rules

A study on speeding violation and driver age produced the following contingency table.

Speeding Age	speeding violation last year	No speeding violation last year
20 -29	95	70
30 -39	101	97
40 -49	70	85
50 -59	45	90
60 -69	19	103

1. Does it appear that being 60 years of age or more and speed violating are mutually exclusive events? Explain your reasoning

If a driver is selected at random from this sample, find the following probabilities:

Round your answers to 3 decimals

2. The driver had a speeding violation in the last year
3. The driver age is less than 50 years
4. The driver is aged between 30 to 39 and had speeding violation last year
5. The driver had no speeding violation last year or is aged between 60 to 69 years
6. The driver had a speeding violation if he is aged between 20 to 29 years
7. The driver had a speeding violation if he is more than 49 years of age.
8. Does it appear that speed violation is independent from age group for this sample of drivers? Explain your reasoning

Part two: Classical probabilities, counting rules and probabilities

1. A fair coin and then a die with 6 sides are tosses find the probabilities of the six events occurring respectively

1. P(Tails)          
2. P(3)                               
3. P(tails and 3)                
4. P(tails | 3)                  
5. P(3 | tails)                       
6. P(4 or a 5)                      

2. An urn contains 5 white ,4 black and 3 red marbles. If 3 marbles are selected from this urn.

Find the probability that at least one of the 3 marbles is black

Answer 1