### Become an OU student

Digital thinking tools for better decision making

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

# 3.1 Taking a chance

Calculating the sizes of sets lets you reason about chances. For example, if a card is picked at random from the pack (that is, any card is as likely to picked as any other), what are the chances that it will be a picture card that is not a heart?

There are 9 picture cards that are not hearts, and 52 cards altogether. Therefore, the chances are 9/52.

For comparing different probabilities with one another, it is very useful to express them as percentages. Here is how to express 9/52 as a percentage using the Python shell.

First, work out 9/52.

Then multiply it by 100, to make it into a percentage.

Finally, round it. One decimal place seems sensible.

>>> 9/52

0.17307692307692307

>>> _*100

17.307692307692307

>>> round(_, 1)

17.3

So, the chances are 17.3%.

Now try this for yourself in the next activity.

## Activity 4 Quick on the draw

A playing card is drawn at random from a full pack. Use the Python console to work out the chances that it will be:

• A heart, but not a picture card.
• Neither a heart nor a picture card.
• Not a picture card.
Active content not displayed. This content requires JavaScript to be enabled.
Interactive feature not available in single page view (see it in standard view).

### Discussion

A heart, but not a picture card: (13 – 3)/52 = 10/52 = 19.2%.

Neither a heart nor a picture card: (52 – 22)/52 = 30/52 = 57.7%.

Not a picture card: (52 – 12)/52 = 40/52 = 76.9%.