Tree Diagrams & Two-Way Tables (Grade 11) — Worksheet & Memo

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Grade 11 · Probability

Tree Diagrams & Two-Way Tables (Grade 11)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 20

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 bag holds 5 red and 3 blue beads. Two are drawn without replacement. Draw the tree diagram and calculate P(both red).
(4)
5/8 × 4/7 = 5/14✓✓✓✓ (4)
2
Using the tree diagram below, calculate P(one of each colour).
(3)
15/56 + 15/56 = 15/28✓✓✓ (3)
3
Using the tree diagram below, calculate P(both blue).
(2)
3/8 × 2/7 = 6/56 = 3/28✓✓ (2)
4
If the two beads were drawn WITH replacement, calculate P(both red).
(2)
5/8 × 5/8 = 25/64✓✓ (2)
5
In the two-way table (Male: 42 bus, 18 walk; Female: 28 bus, 12 walk), calculate P(female).
(2)
40/100 = 0,4✓✓ (2)
6
For the same table, calculate P(walks to school).
(2)
30/100 = 0,3✓✓ (2)
7
For the same table, determine whether 'male' and 'bus' are independent.
(3)
P(M) × P(B) = 0,6 × 0,7 = 0,42 and P(M and B) = 0,42, so yes, they are independent.✓✓✓ (3)
8
State the rule for multiplying along a tree and adding between paths.
(2)
Multiply along a path (AND); add between paths (OR).✓✓ (2)

TOTAL: 20 marks