Probability: Venn Diagrams & the Addition Rule (Grade 10)

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Grade 10 · Probability

MEMORANDUM

Name:

Class:

Date:

Mark

/ 22

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
A fair die is rolled. Find P(rolling a 4).
(1)
1/6✓ (1)
2
Find P(rolling an even number) on a fair die.
(1)
3/6 = 1/2✓ (1)
3
If P(A) = 0,3 find P(not A).
(1)
1 − 0,3 = 0,7✓ (1)
4
State the addition rule.
(2)
P(A or B) = P(A) + P(B) − P(A and B)✓✓ (2)
5
If A and B are mutually exclusive, what is P(A and B)?
(1)
0✓ (1)
6
From the Venn diagram, find P(A and B).
(2)
8/35✓✓ (2)
7
From the Venn diagram, find P(A or B).
(2)
30/35 = 6/7✓✓ (2)
8
From the Venn diagram, find P(neither A nor B).
(2)
5/35 = 1/7✓✓ (2)
9
n(A) = 20 and 8 are in both. How many take ONLY A?
(2)
20 − 8 = 12✓✓ (2)
10
A die is rolled 90 times and a 5 comes up 12 times. Calculate the relative frequency of rolling a 5.
(2)
12/90 ✓ = 2/15 ≈ 0,13 ✓(2)
11
For that same die, write down the theoretical probability of rolling a 5 and comment on the difference.
(2)
1/6 ≈ 0,17 ✓; the relative frequency 0,13 is a little lower, which is normal variation over only 90 rolls ✓(2)
12
What generally happens to the relative frequency as the number of trials becomes very large?
(2)
It tends to settle close to the theoretical probability ✓ — though it need not move closer after every single trial, because chance variation remains ✓(2)
13
Give ONE example of a situation where the probability CANNOT be found by counting equally likely outcomes, and say why.
(2)
Dropping a drawing pin or a bottle top ✓ — the outcomes are not equally likely, so there are no equal outcomes to count; the probability is estimated from an experiment instead (relative frequency) ✓(2)

TOTAL: 22 marks