Probability: Venn Diagrams & Rules (Grade 11) — Worksheet & Memo

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Grade 11 · Probability

Probability: Venn Diagrams & Rules (Grade 11)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 24

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
In the Venn diagram below, 40 learners were surveyed. Determine n(A).
(2)
15 + 8 = 23✓✓ (2)
2
Using the Venn diagram below, calculate P(A and B).
(2)
8/40 = 0,20✓✓ (2)
3
Using the Venn diagram below, calculate P(A or B).
(2)
(15 + 8 + 12)/40 = 35/40 = 0,88✓✓ (2)
4
Using the Venn diagram below, calculate the probability that a learner takes neither A nor B.
(2)
5/40 = 0,13✓✓ (2)
5
P(A) = 0,4, P(B) = 0,5 and P(A and B) = 0,2. Are A and B independent? Show your working.
(3)
P(A) × P(B) = 0,4 × 0,5 = 0,2 = P(A and B), so yes, they are independent.✓✓✓ (3)
6
P(A) = 0,3, P(B) = 0,45 and A and B are mutually exclusive. Calculate P(A or B).
(2)
0,3 + 0,45 − 0 = 0,75✓✓ (2)
7
If P(A) = 0,62, calculate P(not A).
(1)
1 − 0,62 = 0,38✓ (1)
8
Explain the difference between mutually exclusive and complementary events.
(2)
Mutually exclusive events cannot happen together, so P(A and B) = 0. Complementary events are mutually exclusive AND cover the whole sample space, so P(A) + P(B) = 1.✓✓ (2)
9
A coin is tossed 400 times and lands heads 214 times. Calculate the relative frequency of heads and comment on whether the coin appears fair.
(2)
214 ÷ 400 = 0,535 ✓; close to the theoretical 0,5 over a large number of trials, so the coin appears fair ✓(2)
10
In a class of 40: 22 play soccer, 18 play netball, 15 play tennis; 9 play soccer and netball, 7 play soccer and tennis, 6 play netball and tennis, and 4 play all three. How many play none of the three?
(4)
Centre 4 ✓; pairs only: 5, 3, 2 ✓; singles: soccer 22 − 5 − 3 − 4 = 10, netball 18 − 5 − 2 − 4 = 7, tennis 15 − 3 − 2 − 4 = 6 ✓; total in at least one = 10 + 7 + 6 + 5 + 3 + 2 + 4 = 37, so none = 40 − 37 = 3 ✓(4)
11
Explain why you must fill a three-event Venn diagram from the CENTRE outwards.
(2)
Each pairwise total already includes the learners who take all three ✓; filling from the centre lets you subtract that overlap so no one is counted twice ✓(2)

TOTAL: 24 marks