Combined & conditional events
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What does A ∪ B mean?
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All Flashcards in Topic 4.6
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4.6.19 cards
What does A ∪ B mean?
The union — elements in A or B (or both).
What does A ∩ B mean?
The intersection — elements in both A and B.
What does A′ mean?
The complement — elements not in A.
When filling a Venn diagram, what do you fill first?
The intersection (the 'both' region), then work outward.
How do you get 'only A' from n(A) and the overlap?
Only A = n(A) − n(A ∩ B).
How do you find a probability from a Venn diagram?
Region count ÷ total in the universal set.
State the addition rule.
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Why does the addition rule subtract P(A ∩ B)?
So the overlap (in both A and B) isn't counted twice.
What is P(A ∪ B) for mutually exclusive events?
P(A) + P(B), because P(A ∩ B) = 0.
4.6.29 cards
What goes on the branches of a tree diagram?
The probability of each outcome at that stage.
How do you find the probability of a path?
Multiply the probabilities along the branches of that path.
What do the branches leaving one point sum to?
1.
How do you find the probability of an event with several paths?
Find each path (multiply along it) and add the matching paths.
What changes for 'without replacement' on a tree?
The second-stage probabilities use reduced totals (one fewer item, one fewer of that type).
With replacement vs without — branch probabilities?
With replacement they repeat each stage; without, they change.
Fast method for 'at least one'?
1 − P(none).
Bag of 3 red, 2 white, drawn with replacement: P(red then red)?
(3/5)(3/5) = 9/25.
Same bag without replacement: P(red then red)?
(3/5)(2/4) = 3/10.
4.6.39 cards
What does it mean for two events to be independent?
One event happening doesn't change the probability of the other.
State the multiplication rule for independent events.
P(A ∩ B) = P(A) × P(B).
How do you test whether A and B are independent?
Check whether P(A ∩ B) equals P(A) × P(B).
What does mutually exclusive mean?
The events cannot both happen, so P(A ∩ B) = 0.
What is P(A ∪ B) for mutually exclusive events?
P(A) + P(B).
Are mutually exclusive events independent?
No — if they can't co-occur, knowing one occurred changes the other's probability, so they are dependent.
Write P(A ∪ B) for independent events.
P(A) + P(B) − P(A)·P(B).
How do you find a missing probability for independent events?
Substitute P(A ∩ B) = P(A)·P(B) into the addition rule and solve.
Independent A, B with P(A)=0.6, P(B)=0.5: P(both)?
0.6 × 0.5 = 0.3.
Topic 4.6 study notes
Full notes & explanations for Combined & conditional events
Math AA SL exam skills
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