Sample Space Diagrams Flashcards

All 6 cards in this deck

What is a sample space (possibility space) diagram?

A list or grid showing all the possible outcomes of an experiment.

How do you list all possible outcomes systematically?

e.g. a coin thrown 3 times

Work in a fixed order, changing the last item first: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

How many outcomes are there in total when two ordinary six-sided dice are rolled?

$36$ ($6 \times 6$).

What are the steps to find a probability using a sample space grid?

e.g. $P(\text{total} = 4)$ when two four-sided spinners are spun

1. Draw a grid with one experiment along the top, the other down the side: $4 \times 4$ grid
2. Fill every cell with the combined outcome (here the total) — $16$ cells
3. $P = \dfrac{\text{cells wanted}}{\text{total cells}} = \frac{3}{16}$

True or false? In a sample space diagram for two dice, the outcomes (2, 5) and (5, 2) are the same outcome and should be counted once.

False.
They are separate cells in the grid and must both be counted.

True or false? When two dice are rolled, every total from 2 to 12 is equally likely.

False.
The 36 outcomes are equally likely, but some totals come from more cells than others.