Probability terms for AQA A-level Maths
This page covers the following topics:
1. Mutually exclusive events
2. Independent events
3. Discrete and continuous distributions
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.
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.
Define discrete data.
Discrete data is numerical data that can only take specific values.
Anna flips an unbiased coin 4 times. Calculate the probability of Anna getting two heads and then two tails.
These events are independent events, therefore the multiplication rule can be used.
P(getting two heads and then two heads) = 0.5 × 0.5 × 0.5 × 0.5 = 0.0625
Are driving to school and being late to school mutually exclusive events? Explain.
Someone can be late to school while driving there, therefore the two events can occur together and they are not mutually exclusive events.
End of page