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Digital thinking tools for better decision making
Digital thinking tools for better decision making

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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


>>> _*100


>>> round(_, 1)


So, the chances are 17.3%.

Now try this for yourself in the next activity.

Activity 4 Quick on the draw

Timing: Allow about 10 minutes

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.
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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%.