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

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 11 · Probability

Probability: Venn Diagrams & Rules (Grade 11)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 16

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)
840 = 0,20✓✓ (2)
3
Using the Venn diagram below, calculate P(A or B).
(2)
15 + 8 + 1240 = 3540 = 0,88✓✓ (2)
4
Using the Venn diagram below, calculate the probability that a learner takes neither A nor B.
(2)
540 = 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.
(2)
P(A)×P(B) = 0,4×0,5 = 0,2 = P(A and B), so yes, they are independent.✓✓ (2)
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).
(2)
1 − 0,62 = 0,38✓✓ (2)
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)

TOTAL: 16 marks