1 of 8 0-day streak

Two-step sample-space tables with and without replacement

Question 1 of 8

No calculator

The positions have the labels 1: ash, 2: cedar, 3: elm

For the first choice, choose one position uniformly at random. Return the chosen position before the second selection. Then choose uniformly from the available positions for the second choice

Let \(E\) be the event that the first selection is ash and the second selection is cedar

Table headings use the original position numbers. A 1 means the pair can occur; a 0 means it cannot

First / second	3	2	1
1	1	1	?
3	?	1	1
2	1	1	1

(a)1 mark

Which option shows the completed table for this two-stage experiment?

Pairs show original position numbers in first-then-second order. × means impossible

First / second	3	2	1
1	{1,3}	{1,2}	{1,1}
3	{3,3}	{2,3}	{1,3}
2	{2,3}	{2,2}	{1,2}

Usable cells: 9

Pairs show original position numbers in first-then-second order. × means impossible

First / second	3	2	1
1	(1,3)	(1,2)	×
3	(3,3)	(3,2)	(3,1)
2	(2,3)	(2,2)	(2,1)

Usable cells: 8

Pairs show original position numbers in first-then-second order. × means impossible

First / second	3	2	1
1	(1,3)	(1,2)	×
3	×	(3,2)	(3,1)
2	(2,3)	×	(2,1)

Usable cells: 6

Pairs show original position numbers in first-then-second order. × means impossible

First / second	3	2	1
1	(1,3)	(1,2)	(1,1)
3	(3,3)	(3,2)	(3,1)
2	(2,3)	(2,2)	(2,1)

Usable cells: 9

(b)2 marks

Complete the missing numerical cells in the table

Row headed 3, column headed 3 Row headed 1, column headed 1

How many possible ordered outcomes are in the two-stage sample space?

Total ordered outcomes Format: whole number

(d)2 marks

Give the exact probability that the first selection is ash and the second selection is cedar. Give an exact fraction

Exact probability

Format: exact fraction