2.4 Probability

1. There are 8 blue balls are in a bag, half as many red as blue and one white. What is the probability of picking a red ball?

$$\begin{array}{lll}P(red)\hfill & =\hfill & \frac{4}{8+4+1}\hfill \\ \hfill & =\hfill & \frac{4}{13}\hfill \end{array}$$

2. Which has the higher probability?

- Rolling a number size on a die or
- Picking a red counter from a bag which has 7 blue, 8 yellow and 3 red counters?

The probability of rolling a six on a die is:

$$\begin{array}{lll}\hfill P(6)& =\hfill & \frac{1}{6}\hfill \\ \hfill & =\hfill & 0.1\dot{6}\hfill \end{array}$$
The probability of picking a red counter from a bag which has 7 blue, 8 yellow and 3 red counters is:

$$\begin{array}{lll}\hfill P(red)& =\hfill & \frac{3}{7+8+3}\hfill \\ \hfill & =\hfill & \frac{3}{18}\hfill \\ \hfill & =\hfill & 0.1\dot{6}\hfill \end{array}$$
Both event have the same chance of occurring.

3. What is the meaning of

**independent events**in probability and put it in context with an example.Independent events mean that an event is not affected by a previous event. i.e. Each flip of a coin is independent because the coin doesn’t know what happened to it before.

## Calculating Probabilities

$$\text{Probability(P)=}\frac{\text{numberoftimesaneventcanoccur}}{\text{totalnumberofpossibleoutcomes}}$$