Theoretical probability predicts the outcome(s) we expect to happen in the long term.
If you toss a coin 10 times, theoretical probability states that you should get fi ve heads and fi ve tails. In real life, this is seldom the case. However, if you toss a coin 10 000 times, you will see results of 50% heads and 50% tails, as predicted by theoretical probability.
Probability of an event not happening
It is important to note that the sum of the probabilities of an event happening and an event not happening must equal 1. If E is an event, then we can write:
P (E happening) + P (E not happening) = 1 P (E happening) = 1 − (E not happening) or
P (E not happening) = 1 − (E happening)
Worked example 2 In Worked example 1, we saw that the probability of rolling the number 3 on a standard die was 1 Calculate the probability of not rolling a 3 on a standard die.
Solution
We usually just say ‘probability’ instead of ‘theoretical probability’.
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Worked example 3
One card is randomly selected from a deck of 52 playing cards. Find the probability that the card selected was (i) an ace, (ii) a red card, (iii) not an ace.
Solution (i)
(ii) (iii)
Fractions should always be expressed in their simplest form.