 Middle Years

# 12.02 Theoretical probability

Worksheet
Theoretical Probability
1

Consider this list of numbers: 2, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 7, 7, 7, 7, 9, 9

a

How many numbers are in the list?

b

A number is chosen from the list at random. Find the probability that it is an odd number.

c

State the number that has the same probability of being picked as 4.

d

A number is chosen from the list at random. State the number that has the highest probability of being chosen.

2

A number between 1 and 20 inclusive is randomly picked. Find:

a

The probability that the number is at least 8.

b

The probability that the number is less than 8.

3

A standard deck of 52 cards is shown below:

If a card is selected at random, find:

a

The probability that it is a red card.

b

The probability that it is a card between 5 and 9 inclusive.

c

The probability that it is a card that is red and has a number between 5 and 9 inclusive.

d

The probability that it is a card that is red or a king.

e

The probability that it is a spade, with a number printed on it.

f

The probability that it is a red card that has a number more than 2 and at most 9.

g

The probability that it is a black or Kings, but not both.

4

A spinner has 4 sectors with a star, 4 sectors with apple, and 2 sectors with an elephant. All the sectors are the same size.

a

Find the probability of spinning an elephant.

b

Find the probability of spinning an apple.

c

Are the two events in parts (a) and (b) mutually exclusive?

d

Are the two events in parts (a) and (b) complementary?

Probability of complimentary events
5

The probability that Victoria will win the major prize in a raffle at the school fete is 0.053. Find the probability that Victoria will not win.

6

The probability of the local football team winning their grand final is 0.36. Find the probability that they won't win the grand final.

7

The probability that it hails today is 0.43. Find the probability that it doesn't hail.

8

A biased coin is flipped, with heads and tails as possible outcomes. Calculate P(\text{heads}) if P(\text{tails})=0.56.

9

A company that makes sprockets guarantees that they will be within 0.5\text { mm} either way of the client's chosen size. There is a probability of 0.968 that a sprocket will be within the allowable size, find the probability that a sprocket won't be within the allowable size.

10

A number between 1 and 100 inclusive is randomly picked. The probability that the number is less than 61 is \dfrac{60}{100}.

a

What is the complement of drawing a number greater than 61?

b

Find the probability that the number is greater than 61.

11

A number between 1 and 50 inclusive is randomly picked. The probability that the number is less than 42 is \dfrac{82}{100}.

a

State the complement of drawing a number less than 42.

b

State the complement of drawing a number that is at least 43.

c

Find the probability that the number is at least 42.

12

The 26 letters of the alphabet are written on pieces of paper and placed in a bag. If one letter is picked out of the bag at random, find the probability of:

a

Not selecting a B.

b

Not selecting a C.

c

Not selecting a K, R or T.

d

Not selecting a K, L or M.

e

Selecting a letter that is not in the word PROBABILITY.

f

Not selecting a T, L, Q, A, K or Z.

g

Not selecting a A, E, I, O or U.

h

Selecting a letter that is not in the word WORKBOOK.

13

A letter is chosen at random from the word ORDERED.

a

State the letter that has the highest probability of not being chosen.

b

Find the probability that the chosen letter is not "D".

14

A standard 6-sided die is rolled once.

a

Find the probability of rolling a prime number.

b

Find the probability of rolling an odd number.

c

Are the two events in parts (a) and (b) mutually exclusive?

d

Are the two events in parts (a) and (b) complementary?

e

The probability of not rolling a 2.

f

The probability of not rolling a 2 or 5.

g

The probability of not rolling an odd number.

h

The probability of not rolling a 9.

i

The probability of not rolling a 1, 2, 3, 4, 5 or 6.

15
a

A bag contains red marbles and blue marbles. Given the probability of drawing a red marble is 21/44, find the probability of drawing a blue marble.

b

Another bag contains 34 red marbles and 35 blue marbles. If a marble is picked at random, find:

i

P(\text{red})

ii

P(\text{Not Red})

16

A bag contains 50 black marbles, 37 orange marbles, 29 green marbles and 23 pink marbles. If a marble is selected at random, find the following probabilities, in simplest form:

a

P(orange)

b

P(orange or pink)

c

P(not orange)

d

P(neither orange nor pink)

17

Mario has a bag of marbles. It contains 3 white marbles and 5 marbles of other colours. Mario picks a marble from the bag without looking.

a

Find the probability that Mario picks a white marble.

b

Find the probability that Mario picks a marble that is not white.

c

Are the two events in parts (a) and (b) mutually exclusive?

d

Are the two events in parts (a) and (b) complementary?

18

A marble is chosen at random from a box containing 4 different colour marbles, red, blue, green and purple. The probability of selecting different colours is given in the table. Find:

a

The probability of not selecting a green marble.

b

The probability of not selecting a blue marble.

c

The probability of selecting a red or purple marble.

d

The probability of not selecting a purple marble.

e

The probability of selecting neither a blue or green marble.

19

A constellation is randomly selected from the eight shown below:

a

Find the probability that the name of the constellation begins with a vowel.

b

The complementary event is selecting a constellation that begins with a consonant. Find the probability of this event.

c

Find the probability that the constellation has 6 or more stars.

d

The complementary event is selecting a constellation that has less than 6 stars. Find the probability of this event.