Sample Space Diagrams Flashcards

All 5 cards in this deck

What are the steps to construct a sample space diagram for the total of two spins?

e.g. two fair 3-sided spinners numbered 1, 2, 3

1. Write the outcomes of one spinner along the top and the other down the side: $1, 2, 3$ each way

2. Fill each cell with the total, e.g. $2$ and $3$ gives $5$

3. The grid has $3 \times 3 = 9$ equally likely outcomes

How do you use a sample space diagram to find a theoretical probability?

e.g. $P(\text{total} = 12)$ when two ordinary dice are rolled

$\dfrac{\text{number of cells giving that outcome}}{\text{total number of cells}}$, so $\dfrac{1}{36}$

How many equally likely outcomes are there when two experiments are combined?

e.g. rolling an ordinary dice and flipping a coin

Multiply the numbers of outcomes: $6 \times 2 = 12$

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

False. The 36 outcomes are equally likely, but six of them give a total of 7 and only one gives 2.

True or false? In the sample space for rolling two dice, $(2,5)$ and $(5,2)$ count as the same outcome.

False. They are two different outcomes and must both be counted.