Probability basics
Practice Flashcards
How do you find the probability of an event with equally likely outcomes?
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All Flashcards in Topic 4.5
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4.5.19 cards
How do you find the probability of an event with equally likely outcomes?
Favourable outcomes ÷ total outcomes: P(A) = n(A)/n(U).
What range must a probability lie in?
Between 0 and 1 inclusive.
What is the complement rule?
P(A′) = 1 − P(A).
How do you find P(at least one)?
Use the complement: 1 − P(none).
How many outcomes are in the sample space for two dice?
36 (6 × 6 ordered outcomes).
In a sample-space grid, do (2,5) and (5,2) count separately?
Yes — they are different ordered outcomes.
How do you find the probability of a sequence of events?
Multiply the probabilities along the chain.
What changes for 'without replacement'?
After each draw the totals reduce — one fewer item and one fewer of the drawn type.
With replacement vs without — what's the difference?
With replacement the probabilities stay the same each draw; without, they change.
4.5.29 cards
What is the expected number of occurrences in n trials?
n × P, where P is the probability of the event each trial.
Can an expected number be a decimal?
Yes — it is a long-run average, not a single count.
What do you do if the probability isn't given directly?
Find P first (from a sample space, proportion or table), then multiply by n.
What does the expected number actually represent?
The average number of occurrences you'd expect over many repeats.
How do you find an expected total amount?
Multiply the average per trial (expected value) by the number of trials n.
Expected number of sixes in 60 rolls of a fair die?
60 × 1/6 = 10.
If P(win) = 0.25 over 40 games, expected wins?
40 × 0.25 = 10.
Is the expected value guaranteed in one run?
No — it is a long-run average, so a single run may differ.
Expected number of heads in 100 fair coin tosses?
100 × 1/2 = 50.
Topic 4.5 study notes
Full notes & explanations for Probability basics
Math AA SL exam skills
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