Yr 11 Discrete probability distributions - Smarter Maths PDF

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3. Probability, MET2 2015 VCE 14 MC ADV: Statistics (Adv), S1 Probability & Probability Distributions (Adv)

Consider the following discrete probability distribution for the random variable

Discrete Probability Distributions (Y11) Teacher: Angeline Staudinger Exam Equivalent Time: 54 minutes (based on HSC allocation of 1.5 minutes approx. per mark)

Questions

The mean of this distribution is

1. Probability, MET2 2007 VCE 19 MC The discrete random variable of is 5.

A. B.

has probability distribution as given in the table. The mean C. D.

4. Probability, MET2 2016 VCE 7 MC The values of

and are

The number of pets, , owned by each student in a large school is a random variable with the following discrete probability distribution.

A. B. C. D.

2. Probability, MET2 2010 VCE 15 MC The discrete random variable

has the following probability distribution.

If two students are selected at random, the probability that they own the same number of pets is A. B. C. D.

If the mean of A. B. C. D.

is 1 then

5. Probability, MET2 2009 VCE 10 MC The discrete random variable

The median of

7. Probability, MET2 2016 VCE 19 MC

has a probability distribution as shown.

Consider the discrete probability distribution with random variable below.

is

The smallest and largest possible values of

A.

shown in the table

are respectively

A.

B.

B.

C.

C.

D.

D.

6. Probability, MET2 2017 VCE 14 MC The random variable

has the following probability distribution, where

8. Probability, 2ADV S1 SM-Bank 1 .

One bag contains red and green balls. Kalyn randomly chooses one ball from the bag. Without replacement, he then chooses a second ball from the bag.

x Pr(X = x)

The variance of A. B. C. D.

is

–1

0

1

p

2p

1 – 3p

Complete the tree diagram below and then draw a probability distribution table for the number of red balls that could be drawn out of the bag. (3 marks)

9. Probability, 2ADV S1 SM-Bank 2 Evaluate

and

in the discrete probability distribution table below, given that

12. Probability, MET1 2010 VCE 8 .

The discrete random variable

has the probability distribution

(3 marks)

10. Probability, MET1 2008 VCE 7 Jane drives to work each morning and passes through three intersections with traffic lights. The number of traffic lights that are red when Jane is driving to work is a random variable with probability distribution given by

Find the value of

(3 marks)

13. Probability, MET1 2012 VCE 4 On any given day, the number of telephone calls that Daniel receives is a random variable with probability distribution given by

a. What is the mode of

?

(1 mark)

b. Jane drives to work on two consecutive days. What is the probability that the number of traffic lights that are red is the same on both days? (2 marks)

11. Probability, MET1 2009 VCE 7 The random variable

has this probability distribution.

a. Find the mean of

Find

b.

(2 marks)

the variance of (3 marks)

(2 marks)

c. Daniel receives telephone calls on both Monday and Tuesday. What is the probability that Daniel receives a total of four calls over these two days? marks)

a.

.

b. What is the probability that Daniel receives only one telephone call on each of three consecutive days? (1 mark)

(3

14. Probability, MET1 2013 VCE 7

Worked Solutions

The probability distribution of a discrete random variable,

, is given by the table below.

1. Probability, MET2 2007 VCE 19 MC

a. Show that b. Let

. .

i. Calculate ii. Find

(3 marks)

. Answer in exact form. .

(2 marks)

(1 mark)

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2. Probability, MET2 2010 VCE 15 MC

3. Probability, MET2 2015 VCE 14 MC

7. Probability, MET2 2016 VCE 19 MC

♦♦♦ Mean mark 15%.

4. Probability, MET2 2016 VCE 7 MC

5. Probability, MET2 2009 VCE 10 MC

6. Probability, MET2 2017 VCE 14 MC

8. Probability, 2ADV S1 SM-Bank 1

10. Probability, MET1 2008 VCE 7 a.

b.

11. Probability, MET1 2009 VCE 7 a.

b.

9. Probability, 2ADV S1 SM-Bank 2

12. Probability, MET1 2010 VCE 8

14. Probability, MET1 2013 VCE 7 a.

13. Probability, MET1 2012 VCE 4

b.i.

a.

b.

♦♦ Part (b)(ii) mean mark 32%.

c. ♦ Mean mark 36%.

ii.

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