DP IB Maths: AA SL

Topic Questions

4.3 Probability

1
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4 marks

The lengths, in cm, of 120 adult platypuses are recorded in the following table:

Length, l
(cm)

Frequency
(female)

Frequency
(male)

 39 less or equal than l less than 42 14 0
42 less or equal than l less than 45 29 0
45 less or equal than l less than 48 12 7
48 less or equal than l less than 51 6 21
51 less or equal than l less than 54 3 19
54 less or equal than l less than 57 1 5
57 less or equal than l less than 60 0 2
60 less or equal than l less than 63 0 1

One platypus is chosen at random.  Find the probability that the platypus is:

(i)
male
(ii)
less than 51 cm long
(iii)
a male less than 45 cm long
(iv)
a female between 45 and 54 cm long.

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2
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4 marks

Two fair spinners each have three sectors numbered 1 to 3. The two spinners are spun together and then the product of the numbers indicated on each spinner is recorded.

Find the probability of the product indicated by the spinners being

(i)
exactly 6
(ii)
less than 4
(iii)
an odd number.

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3a
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3 marks

The Venn diagram below shows the probabilities of members of an exotic sports society participating in various activities.

A represents the event that the member participates in aerial yoga.

B represents the event that the member participates in bog snorkelling.

C represents the event that the member participates in cheese rolling.

ib3a-ai-sl-4-3-ib-maths-medium

Given that the probability of a member participating in cheese rolling is 0.44,

determine the values of

(i)

x

(ii)
y
3b
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2 marks

Determine the probability that a member of the society

(i)

participates in at least one of the three activities

(ii)
participates in exactly one of the three activities.

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4a
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3 marks

The following Venn diagram shows the number of adults in a poll who said they enjoy watching action films (A), Bollywood musicals (B), and crime thrillers (C).

q4a-4-3-probability-medium-ib-ai-sl-maths

100 adults were polled in total.

One of the adults who was polled is selected at random. Given that the adult chosen enjoys watching at least one of those three genres of film, find the probability that the adult enjoys watching:

(i)
Bollywood musicals
(ii)
only one of the three genres of film
(iii)
exactly two of the three genres of film.
4b
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4 marks

Find the following probabilities:

(i)
P left parenthesis A intersection C right parenthesis
(ii)
P left parenthesis A union C right parenthesis
(iii)
P left parenthesis C vertical line B right parenthesis
(iv)
P left parenthesis B to the power of apostrophe right parenthesis

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5
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4 marks

On any given day the probability that Radigast has a lichen smoothie with his lunch is 0.4, and the probability that he has a wild mushroom wrap is 0.8.  Given that the probability of him having both those items is 0.35, find the probability that Radigast has:

(i)
a wild mushroom wrap but not a lichen smoothie
(ii)
neither a wild mushroom wrap nor a lichen smoothie.

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6a
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2 marks

A and B are two events such that P left parenthesis A right parenthesis equals 0.35 commaP left parenthesis B right parenthesis equals 0.25 space space and P left parenthesis A space union space B right parenthesis equals 0.6. State, with a reason, whether A and are mutually exclusive.

6b
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2 marks

C and D are two events such that  P left parenthesis C right parenthesis equals 0.2,P left parenthesis D right parenthesis equals 0.4  and P left parenthesis C space intersection space D right parenthesis equals 0.18 State, with a reason, whether C and D are independent.

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7a
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3 marks

A bag contains 13 yellow tokens and 7 green tokens. Two tokens are drawn from the bag without replacement.

Draw a tree diagram to represent this experiment.

7b
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3 marks

Find the probability that the two tokens drawn are the same colour.

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8a
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4 marks

A,B  and C are three events with  P left parenthesis A right parenthesis equals 0.2P left parenthesis B right parenthesis equals 0.25P left parenthesis C right parenthesis equals 0.6   and   P left parenthesis B intersection C right parenthesis equals 0.08.

Given that events A and C are mutually exclusive, and that events A and B are independent, draw a Venn diagram to illustrate the probabilities.

8b
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6 marks

Find:

(i)

P left parenthesis A to the power of apostrophe intersection C to the power of apostrophe right parenthesis

(ii)

P left parenthesis left parenthesis A intersection B to the power of apostrophe right parenthesis union C right parenthesis

(iii)
P left parenthesis A to the power of apostrophe union left parenthesis B intersection C right parenthesis to the power of apostrophe right parenthesis

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9a
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4 marks

Three events,A , B and C, are such that B and C are mutually exclusive and A and C are independent.  P left parenthesis A right parenthesis equals 0.3P left parenthesis B right parenthesis equals 0.45  and  P left parenthesis C right parenthesis equals 0.1.

Given that P left parenthesis left parenthesis A union B union C right parenthesis to the power of apostrophe right parenthesis equals 0.43, draw a Venn diagram to show the probabilities for events A,B and C.

9b
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6 marks

Find:

(i)

P left parenthesis B vertical line A right parenthesis

(ii)

P left parenthesis A vertical line B to the power of apostrophe right parenthesis

(iii)
P left parenthesis A vertical line left parenthesis B union C right parenthesis right parenthesis

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10a
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4 marks

Given that P left parenthesis A right parenthesis equals 0.27P left parenthesis B right parenthesis equals 0.39   and P left parenthesis A intersection B right parenthesis equals 0.21 , find:

(i)       P left parenthesis A union B right parenthesis

(ii)
P left parenthesis B vertical line A right parenthesis
10b
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2 marks

The event C has P left parenthesis C right parenthesis equals 0.19 .  The events A and C are mutually exclusive. 

Given that space P left parenthesis B intersection C right parenthesis equals 0.04, find P left parenthesis A union B union C right parenthesis.

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11a
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3 marks

Ichabod is a keen chess player who plays one game of chess online every night before going to bed.  In any one of those games, the probabilities of Ichabod winning, drawing, or losing are 0.4, 0.27 and 0.33 respectively. Following each game, the probabilities of Ichabod sleeping well after winning, drawing or losing are 0.7, 0.9 and 0.2 respectively.

Draw a tree diagram to represent this information.

11b
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4 marks

Find the probability that on a randomly chosen night

(i)
Ichabod loses his chess game and sleeps well

(ii)
Ichabod sleeps well.
11c
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4 marks

Given that Ichabod sleeps well, find the probability that his chess game did not end in a draw.

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