X(no.of hours)	0.5	1	1.5	2	2.5	3	3.5	4
P(x)	0.02	0.1	0.35	0.22	0.15	0.12	0.03	0.01

A car examination depot has collected the following information on how long people take to get their certificate of fitness or other documents renewed

Verify that this is a discrete probability distribution.

2. Find the probability that a person waits for:

• Exactly 1 hour
• At least 2 hours

3. Find the expected value of the time a person waits for.

4. Find the variance.

5. Find the standard deviation.

3. The probability of Andre getting a haircut this week is 0.72. The

probability of his brother getting a haircut this week is 0.55. Assuming

independence, find the probability of them:

A. Both getting a haircut this week.

B. Neither of them getting a haircut this week.

C. Only one of them getting a haircut this week.

Question 2.

At the Hospital, the following data were collected on a survey on 1,000 patients.

	Smoke Ganja	Do not smoke ganja
Have an alcohol problem	128	34
Do not have an alcohol problem	192	646

Find the probability that a patient:

a) smokes ganja or has an alcohol problem.

b) has an alcohol problem, given that he smokes ganja.

c) has an alcohol problem .

d) does not smoke ganja given that he does not have an alcohol

problem.

A bag has 30 sweets: 10 strawberry, 15 melon and 5 cherry sweets.

Two sweets were randomly taken, one after the other, without

replacement.

a) Draw a properly labelled tree diagram to show this.

b) Find the probability of drawing a melon sweet and a cherry sweet

in any order.

Drivers' licence applicants from Classic Driving school have an 85%

chance of passing the driver's test. Seven applicants from Classic

Driving school do the test at the depot. Assuming the results are

binomially distributed, find the probability of success for:

a) Exactly 2 applicants .

b) At most 2 applicants .

c) At least 3 applicants.

d) All the applicants.