AQA · Mathematics · 8300
GCSE Maths: Probability: independent events
Probability · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Probability: independent events (Corbettmaths Video 249), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
18 flashcards · Free to study · No account needed
Study this deck
Preparing your cards…
All questions and answers
Read through the full deck, or practise recalling each answer above.
What is the formula for the probability of two independent events both occurring?
Show answer
Multiply the individual probabilities: P(A and B) = P(A) × P(B)
What is the probability of a fair coin landing on heads twice in two flips?
Show answer
1/4 (or 0.25). Calculate as (1/2) × (1/2) = 1/4
If a fair six-sided dice is rolled three times, what is the probability of getting a six all three times?
Show answer
1/216. Calculate as (1/6) × (1/6) × (1/6) = 1/216
Why does replacing an item before selecting again ensure events are independent?
Show answer
Replacement restores the original probabilities, so the outcome of the first selection does not affect the second selection
If event A has probability 0.7 and event B has probability 0.4, what is the probability both occur (assuming independence)?
Show answer
0.28. Calculate as 0.7 × 0.4 = 0.28
If the probability of an event occurring is p, what is the probability of it NOT occurring?
Show answer
1 - p (the complement probability)
If the probability of hitting a bullseye is 0.3, what is the probability of NOT hitting the bullseye with two darts?
Show answer
0.49. Calculate as 0.7 × 0.7 = 0.49 (where 0.7 is the probability of missing)
If a biased coin has probability 0.7 of landing on tails, what is the probability it lands on heads twice in two flips?
Show answer
0.09. Calculate as 0.3 × 0.3 = 0.09 (where 0.3 = 1 - 0.7 is the probability of heads)
What does 'at least one' mean when calculating probabilities?
Show answer
One or more occurrences. Often easier to calculate as 1 minus the probability of none occurring
If a fair dice is rolled three times, what is the probability of getting NO sixes?
Show answer
125/216. Calculate as (5/6) × (5/6) × (5/6) = 125/216
How do you find the probability of 'exactly once' in multiple independent trials?
Show answer
Use the binomial approach: multiply the probability of one success and all other failures, then multiply by the number of ways to arrange that outcome.
What does 'at least two' mean when calculating probabilities?
Show answer
Two or more. It includes exactly two, exactly three, etc., up to all possible occurrences.
If three independent events have probabilities 4/5, 2/3, and 3/4, what is the probability all three occur?
Show answer
(4/5) × (2/3) × (3/4) = 2/5 or 0.4
What is the complement of 'all three dice show a 6'?
Show answer
At least one die does not show a 6 (or equivalently, none of them all show 6).
If the probability that all 3 biased dice show a 6 is 0.343, and each die is identical, what is the probability one die shows a 6?
Show answer
0.7, because 0.7³ = 0.343, so P(one die shows 6) = ∛0.343 = 0.7
When finding if a score from multiple independent trials is even, what strategy should you use?
Show answer
Consider the parity (odd/even) of each outcome and determine which combinations sum to an even number.
If beads are in the ratio 1:3 (yellow to green), what is the probability of selecting a yellow bead?
Show answer
1/4, because there is 1 yellow for every 4 total beads (1 yellow + 3 green).
If a spinner lands on blue twice with probability 9/400, what is the probability it lands on blue once?
Show answer
3/20 (or 0.15), because if P(blue)² = 9/400, then P(blue) = √(9/400) = 3/20.
Want to create your own cards? Create a free account. AI generation uses credits.