1 of 8 0-day streak

Represent a multi-stage finite sample space

Question 1 of 8

No calculator

A finite experiment has 2 stages. The stage choices are independent

At the first stage, the possible outcomes are square, circle, triangle. Their branch probabilities are \(\text{square}: \frac{1}{3}\), \(\text{circle}: \frac{1}{3}\), \(\text{triangle}: \frac{1}{3}\)

At the second stage, the possible outcomes are square, circle, triangle. Their branch probabilities are \(\text{square}: \frac{1}{3}\), \(\text{circle}: \frac{1}{3}\), \(\text{triangle}: \frac{1}{3}\)

Let \(S\) be the sample space of ordered stage outcomes

Let \(E\) be the event that the last-stage outcome is square

(a)1 mark

Which option is the only representation of \(S\) that lists every ordered outcome exactly once?

Grid

Each row records one ordered outcome
first stage	second stage	Ordered outcome
square	square	(square, square)
square	circle	(square, circle)
square	triangle	(square, triangle)
circle	square	(circle, square)
circle	circle	(circle, circle)
circle	triangle	(circle, triangle)
triangle	square	(triangle, square)
triangle	circle	(triangle, circle)
triangle	triangle	(triangle, triangle)

Ordered list

(square, square)
(square, circle)
(square, triangle)
(circle, square)
(circle, circle)
(circle, triangle)
(triangle, square)
(triangle, circle)

Probability tree

If needed, scroll sideways to follow each complete path

(b)3 marks

Complete the missing values in the record

Complete the missing values
Quantity	Value
first stage choices	3
second stage choices	?
Total ordered outcomes	?
Favourable outcomes	?

Favourable outcomes second stage choices Total ordered outcomes

What is the exact probability that the stated event occurs?

Exact probability

Format: exact fraction or terminating decimal