What's covered
Key facts
Binomial distribution
The probability that all n trials are successes is p to the power n, e.g. 0.99 to the power 5 = 0.951 (3 sf).
Expected frequency and risk
Absolute risk is the probability of the event in one group, found from collected data as number affected / number in the group.
Normal distribution
Values more than three standard deviations from the mean are very unusual (about 99.7% lie within three).
Probability scale and relative frequency
Higher tier: differences between experimental and theoretical values are commented on in terms of possible bias; formal significance tests are not required, and a small difference can arise by chance.
Tree diagrams, independence and conditional probability
P(at least one) = 1 - P(none), since "none" and "at least one" cover every outcome with no overlap.
Two-way tables, sample spaces and Venn diagrams
A set of events is exhaustive if at least one of them has to occur whenever the experiment is carried out (they cover every possible outcome).
Binomial distribution
A binomial model needs a fixed number of trials, only two possible outcomes on each trial, a constant probability of success, and independent trials.
Expected frequency and risk
Expected frequency of a characteristic = probability x number in the sample or population (or number of trials).
Normal distribution
Approximately 68% (just over two thirds) of the data lie within one standard deviation of the mean.
Probability scale and relative frequency
For a fair dice rolled 600 times the theoretical expectation is 600 x 1/6 = 100 of each score, so a result far from this suggests bias.
Practice questions with answers
A taste of the 58 questions in this topic, answers marked. Sign up to practise the full set with spaced repetition.
Which of these is NOT a condition for a binomial model?
- ✓Each trial has more than two outcomes
- •The probability of success stays the same
- •The trials are independent of each other
- •There is a fixed number of trials
The relative risk of failing for course A compared with course B is 0.75. What does this mean?
- •75% of people who took course A failed
- •The risk of failing is 25% higher after course A
- ✓The risk of failing is 25% lower after course A
- •The risk of failing is 75% lower after course A
Which data set is most suitable for a Normal model?
- •Categorical data with one very common category
- •Continuous data where the mean is far above the median
- ✓Continuous, symmetrical data with a bell-shaped histogram
- •Discrete counts with a strong positive skew
Which of these values cannot be a probability?
- •0
- •0.99
- •1
- ✓1.2
Which equation shows that events A and B are independent?
- •P(A and B) = 0
- •P(A and B) = P(A) + P(B)
- ✓P(A and B) = P(A) x P(B)
- •P(A) + P(B) = 1
Which formula gives P(A or B) for any two events A and B?
- ✓P(A) + P(B) - P(A and B)
- •P(A) + P(B) - P(A) x P(B)
- •P(A) + P(B) + P(A and B)
- •P(A) x P(B) - P(A and B)
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