9709 · 5.3
Probability flashcards
Revision flashcards for Cambridge 9709 Probability (syllabus 5.3). Flip, recall, then mark a real past-paper question.
Card
What is the range of a probability value?
A probability $P(A)$ must be between 0 and 1, inclusive. $0 \le P(A) \le 1$.
Card
What is a 'sample space'?
The set of all possible outcomes of an experiment. Denoted by $S$ or $\Omega$.
Card
What is the formula for a complementary event, $A'$?
$P(A') = 1 - P(A)$. This is the probability that event A does *not* occur.
Card
What are 'mutually exclusive' events?
Events that cannot happen at the same time. If A and B are mutually exclusive, then $P(A \cap B) = 0$.
Card
What is the addition rule for two mutually exclusive events, A and B?
$P(A \cup B) = P(A) + P(B)$.
Card
What are 'independent' events?
The occurrence of one event does not affect the probability of the other. For independent events A and B, $P(A|B) = P(A)$.
Card
What is the multiplication rule for two independent events, A and B?
$P(A \cap B) = P(A) \times P(B)$.
Card
What is the general addition rule for any two events, A and B?
$P(A \cup B) = P(A) + P(B) - P(A \cap B)$. This accounts for any overlap.
Card
What does the notation $P(A|B)$ mean?
The conditional probability of A occurring, *given that* B has already occurred.
Card
What is the formula for conditional probability, $P(A|B)$?
$P(A|B) = \frac{P(A \cap B)}{P(B)}$.
Card
Common Trap: Can two events with non-zero probabilities be both mutually exclusive and independent?
No. If they are mutually exclusive, $P(A \cap B) = 0$. If they were also independent, this would require $P(A) \times P(B) = 0$, which means at least one event must have zero probability.