2.5 Relative Frequency

The table shows the relative frequency of a 5 sided spinner.

Side |
Chance |

Green | 0.1 |

Blue | 0.3 |

Red | 0.2 |

Black | ?? |

Yellow | ?? |

1. How many times would you expect the spinner land on the blue side if

you spun the spinner 200 times?

A probability of 0.3 is means that the spinner will land on the blue side 30% of the time.

$$\begin{array}{lll}\hfill frequency& =\hfill & 0.3\times 200\hfill \\ \hfill & =\hfill & 60\hfill \end{array}$$

2. If the probability of the black and the yellow are equal, what are their probabilities.

The sum of all the possible outcomes is always 1. Therefore:

$$P(\text{green})+P(\text{blue})+P(\text{red})+2P(x)=1$$
Since
$p(x)=P(black)\text{orP(yellow)}$

.

Rearranging and substituting the known values allows calculation of
$p(\text{x)}$
$$\begin{array}{lll}\hfill P(\text{x})& =\hfill & \frac{1-P(\text{green})-P(\text{blue})-P(\text{red})}{2}\hfill \end{array}$$
=
1 − 0.1 − 0.3 − 0.2
2
=
0.2

So the probability of getting a black is 0.2 and yellow is also 0.2.

## Sum of all possible outcomes

The sum of all the outcomes of an event is **always** 1.0.

i.e. the probability of an event not occurring is:

$$\begin{array}{lll}\hfill P(\text{nothappening})& =\hfill & 1-P(\text{happening})\hfill \end{array}$$