Calculating Probabilities

This lesson covers calculating probabilities for single events, listing outcomes systematically, using sample spaces, and applying the complementary event rule. These skills are essential for the Edexcel GCSE Mathematics (1MA1) specification and appear frequently on all three exam papers.

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Single Event Probabilities

For any single event with equally likely outcomes:

P(event) = number of favourable outcomes / total number of outcomes

Worked Example 1

A standard pack of 52 playing cards is shuffled and one card is drawn at random. Find the probability that the card is:

(a) a heart (b) a king (c) the queen of spades

Solution:

(a) There are 13 hearts in a pack of 52 cards. P(heart) = 13/52 = 1/4

(b) There are 4 kings in a pack of 52 cards. P(king) = 4/52 = 1/13

(c) There is exactly 1 queen of spades. P(queen of spades) = 1/52 = 1/52

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Listing Outcomes Systematically

When working with probability, it is essential to list all possible outcomes in a systematic (organised) way so that none are missed or counted twice.

Worked Example 2