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: south, 2: west, 3: centre

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

Let \(E\) be the event that the first selection is west and the second selection is south

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

Second / first	3	2	1
3	1	?	1
2	?	1	1
1	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

Second / first	3	2	1
3	(3,3)	(2,3)	(1,3)
2	(3,2)	(2,2)	(1,2)
1	(3,1)	(2,1)	(1,1)

Usable cells: 9

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

Second / first	3	2	1
3	×	(2,3)	(1,3)
2	(3,2)	×	(1,2)
1	(3,1)	(2,1)	×

Usable cells: 6

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

Second / first	3	2	1
3	{3,3}	{2,3}	{1,3}
2	{2,3}	{2,2}	{1,2}
1	{1,3}	{1,2}	{1,1}

Usable cells: 9

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

Second / first	3	2	1
3	(3,3)	(2,3)	(1,3)
2	(3,2)	(2,2)	×
1	(3,1)	(2,1)	(1,1)

Usable cells: 8

(b)2 marks

Complete the missing numerical cells in the table

Row headed 2, column headed 3 Row headed 3, column headed 2

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 west and the second selection is south. Give an exact fraction

Exact probability

Format: exact fraction