Counting Principles & Probability (Grade 12) — Worksheet & Memo

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Grade 12 · Probability

Counting Principles & Probability (Grade 12)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 29

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
How many 4-digit PINs can be formed if digits may repeat?
(2)
10⁴ = 10 000✓✓ (2)
2
How many 4-digit PINs can be formed if no digit may repeat?
(2)
10 × 9 × 8 × 7 = 5 040✓✓ (2)
3
In how many ways can 5 different books be arranged on a shelf?
(1)
5! = 120✓ (1)
4
4 boys and 3 girls sit in a row. In how many ways can they sit if the girls sit together?
(3)
5! × 3! = 120 × 6 = 720✓✓✓ (3)
5
For those 7 learners, calculate the probability that the girls sit together.
(2)
720/(5 040) = 1/7✓✓ (2)
6
How many arrangements are there of the letters of the word LETTER?
(3)
(6!)/(2!×2!) = 180✓✓✓ (3)
7
Write down the value of 0!
(1)
1✓ (1)
8
Using the tree diagram below, calculate the probability that a person tests positive.
(3)
1/5 × 9/10 + 4/5 × 2/10 = 0,34✓✓✓ (3)
9
Of 80 learners: 40 play soccer, 32 play cricket, 28 play tennis; 15 play soccer and cricket, 12 soccer and tennis, 10 cricket and tennis, and 6 play all three. How many play none?
(4)
Centre 6 ✓; pairs only 9, 6, 4 ✓; singles: soccer 40 − 9 − 6 − 6 = 19, cricket 32 − 9 − 4 − 6 = 13, tennis 28 − 6 − 4 − 6 = 12 ✓; at least one = 19 + 13 + 12 + 9 + 6 + 4 + 6 = 69; none = 80 − 69 = 11 ✓(4)
10
In a group of 150 people, 90 are female and 60 wear glasses, of whom 40 are female. Determine whether ‘female’ and ‘wears glasses’ are independent.
(4)
P(F) = 90/150 = 0,6 ✓; P(G) = 60/150 = 0,4 ✓; P(F and G) = 40/150 = 0,267 ✓; P(F) × P(G) = 0,24 ≠ 0,267, so NOT independent ✓(4)
11
State the test for two events being independent.
(2)
P(A and B) = P(A) × P(B) ✓✓(2)
12
Why must a three-event Venn diagram be filled from the centre outwards?
(2)
Each pairwise total already includes those in all three ✓; starting at the centre lets you subtract that overlap so nobody is counted twice ✓(2)

TOTAL: 29 marks