Calculating Probability - With Answers

7/29/2019 Calculating Probability - With Answers

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WorkSHEET 12.1 Introducing probability Name: ___________________________

1 A card is drawn from a pack of 52 playing

cards. What is the probability the card drawn is:

(a) a red card?

(b) a heart?

(c) an ace?

26(a) P(red)

52

1

2

=

=

13(b) P(heart)

52

14

=

=

4(c) P(ace)

52

1

13

=

=

2 Two dice are rolled.

What is the probability that:(a) the first die shows a 6?

(b) the second die shows an odd number?

1(a) P(6)

6=

3(b) P(odd)

6

1

2

=

=

© John Wiley & Sons Australia, Ltd Page 1



3 120 Year 10 students are surveyed on subject

satisfaction.

90 students like Maths and 105 students like

English.

80 students like both subjects.

What is the probability that a student selected

at random likes:

(a) English

(b) English only

(c) neither Maths nor English?

English only = 105 – 80

English only = 25

Maths only = 90 – 80

Maths only = 10

Neither Maths nor English = 120 − 80 – 25 – 10

Neither Maths nor English = 5

(a) P(English) =120

105

Pr (English =8

7

(b) P(English only) =120

25

Pr (English only=24

5

(c) P(neither Maths nor English) =120

5

(neither Maths nor English =24

1




4 Write the following odds as probabilities:

(a) 4–1

(b) 2–5

(c) 1–1

(a) 4–1

5

1

14

1

=

+

=

(b) 2–5

7

5

52

5

=

+

=

(c) 1–1

2

1

11

1

=

+

=

5 Write the following probabilities as odds:

(a)4

1

(b)10

3

(a)31

141

+

=

= 3–1

37

3

10

3) b(

+

=

= 7–3

6 State the event that is complementary to each

of the following:

(a) a coin landing Heads

(b) rolling less than 4 with a die

(c) selecting an ace from a standard deck.

(a) A coin landing Tails

(b) Rolling more than 3

(c) Not selecting an ace




7 The weather bureau forecasts the chance of rain

for the next day as 60%. What is the probability

of it not raining the next day?

P(rain) 60%

60100

P(not raining) 1 P(rain)

601

100

31

5

2

5

=

=

= −

= −

= −

=

8 A set of cards is numbered

{1, 2, 3, 4 … 24, 25}. A card is selected at

random. Find:

(a) P(not an even number)

(b) P(not a multiple of 5).

(a) P(not an even number)

= 1 − P(even number)

= 1 − 25

12

=25

13

(b) P(not a multiple of 5)

= 1 − P(multiple of 5)

= 1 − 25

5

=5

4




9 A bag contains 30 balls of which 12 are red,

7 are blue and the rest black. Find:

(a) P(not black)

(b) P(neither red nor black).

Number of black balls = 30 – 12 – 7

Number of black balls = 11

(a) P(not black) = 1 – P(black)

Pr (no black = 1 − 30

11

Pr (no black =30

19

(b) P(neither red nor black)

= 1 − P(red or black)

= 1 − 30

23

=30

7

or

P(neither red nor black) = P(blue)

=30

7

10 A raffle has 500 tickets. Kylie, Nicholas, Sergei

and Damian purchased 120 tickets between

them. What is the probability that none of them

wins?

P(not winning) = 1 − P(winning)

= 1 − 500

120

=25

19


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Calculating Probability - With Answers