Probability terms for AQA GCSE Maths
This page covers the following topics:
1. Mutually exclusive events
2. Independent events
3. Discrete and continuous distributions
4. Exhaustive set of outcomes
Mutually exclusive events are events that cannot occur at the same time. This means that the probability of two mutually exclusive events occuring together is 0. The addition rules states that the probability of either of two mutually exclusive events occuring is the sum of the individual probabilities of the two events.
Independent events are ones which are not affected by previous ones. The multiplication rule states that the probability of two independent events occuring is the product of the individual probabilities of the two events.
Discrete data is numerical data that can only take specific values and is presented on a frequency table where the frequency of each value for a given data set is counted. Continuous data is numerical data that can take any value within a given range. Continuous data is presented in a grouped frequency table, since there are infinitely many possibilities of the values of it, due to the fact that it can take any value.
An exhaustive set of events are events which cover all possible outcomes. Adding the probabilities of an exhaustive set of events will always add up to 1.
A two-sided coin is biased. Flipping a tails has a probability of 0.55. Calculate the probability of flipping a heads.
Using the addition rule, 1 = 0.55 + P(Heads), therefore P(Heads) = 1 − 0.55 = 0.45.
An unbiased die is thrown 3 times. Calculate the probability of getting a 1, then a 3 and then a 5.
The three events are independent events. Therefore, the multiplication rule can be used.
P(getting a 1, a 3 and a 5) = 1/6 × 1/6 × 1/6 = 1/216.
Explain whether rolling an odd number and an even number when a die is thrown is exhaustive.
Rolling an odd number includes 1, 3 and 5.
Rolling an even number includes 2, 4 and 6.
This covers all the possible outcomes of rolling a die, therefore these events are exhaustive.
Define discrete data.
Discrete data is numerical data that can only take specific values.
Given that the probability of Harry being late for school is 0.25, calculate the probability of him not being late.
Being late and not being late to school are exhaustive, therefore the sum of their probabilities is 1.
So, P(late) + P(not late) = 1.
0.25 + P(not late) = 1, therefore P(not late) = 0.75.
End of page