Combined Events and Conditional ProbabilityEdexcel GCSE Maths: Flashcards

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What is the addition rule for probability?

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What is the addition rule for probability?: P(A or B) = P(A) + P(B) − P(A and B). This rule accounts for the overlap between events A and B to avoid counting the intersection twice.
Define mutually exclusive events.: Events that cannot occur at the same time. If A and B are mutually exclusive, then P(A and B) = 0, so P(A or B) = P(A) + P(B).
Define independent events.: Events where the outcome of one event does not affect the probability of the other event occurring. For independent events A and B: P(A and B) = P(A) × P(B).
What is conditional probability and what does P(B|A) mean?: Conditional probability is the probability of event B occurring given that event A has already occurred. P(B|A) represents 'the probability of B given A'.
State the multiplication rule for conditional probability.: P(A and B) = P(A) × P(B|A). This calculates the probability of both events occurring, where P(B|A) is the probability of B given that A has happened.
How do you use a tree diagram to represent independent events?: Draw branches from a starting point for each outcome of the first event. From each of these, draw branches for outcomes of the second event. The probability on each branch remains the same regardless of previous outcomes. Multiply along branches to find combined probabilities.
How do you use a tree diagram to represent dependent events?: Draw branches for the first event. From each outcome, draw branches for the second event, but the probabilities on these secondary branches change depending on which first outcome occurred. This reflects that the events are dependent.
What is set notation in probability and name three common symbols.: Set notation describes collections of outcomes. Key symbols: ∪ (union/or), ∩ (intersection/and), ' (complement/not), ⊂ (subset). For example, A ∩ B represents outcomes in both A and B.
How do Venn diagrams represent probabilities of combined events?: Venn diagrams use overlapping circles to show events. Each region represents a different outcome combination. P(A and B) is shown in the overlapping region, non-overlapping regions show P(A only) and P(B only).
Explain how to use systematic listing to solve probability problems.: List all possible outcomes in an organised, methodical way (such as in a table or tree structure). Count outcomes matching the required event and divide by total outcomes. Ensures no outcomes are missed or counted twice.
For events A and B, when is P(A and B) = 0?: When events A and B are mutually exclusive. This means they cannot both occur at the same time, so their intersection is empty.
If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, what is P(A and B)?: P(A and B) = P(A) × P(B) = 0.4 × 0.6 = 0.24. For independent events, simply multiply the individual probabilities.
What must you check before using P(A and B) = P(A) × P(B)?: You must verify that events A and B are independent. This rule only applies when the occurrence of one event does not affect the probability of the other event.
How do you calculate P(B|A) from P(A and B) and P(A)?: P(B|A) = P(A and B) ÷ P(A). This rearranges the multiplication rule to isolate the conditional probability.
In a Venn diagram with events A and B, how do you find P(A or B)?: P(A or B) = P(A) + P(B) − P(A and B). This is the sum of probabilities in region A only, region B only, and the overlapping region (intersection).