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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.

$frequency = 0.3×200 = 60$

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:
$P(green)+P(blue)+P(red)+2P(x)=1$
Since

.

Rearranging and substituting the known values allows calculation of $p(x)$ $P(x) = 1−P(green)−P(blue)−P(red) 2$

= 10.10.30.2 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:

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