Probability Diagrams (Tree & Venn Diagrams)Cambridge IGCSE Maths: Flashcards

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What is a sample space diagram used for?

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What is a sample space diagram used for?: To list every possible outcome of a combined event, so probabilities can be counted directly
Two fair dice are rolled. How many total equally likely outcomes are there?: 36 (6 x 6)
On a tree diagram, what must probabilities on branches from the same point sum to?: 1
How do you find the probability of a combined outcome along one path of a tree diagram?: Multiply the probabilities along that path's branches
How do you find the probability of two different outcomes on a tree diagram?: Add the probabilities of each separate path
What happens to branch probabilities when selecting without replacement?: They change on later branches because the total number of items (and possibly favourable items) decreases
What stays the same about branch probabilities when selecting with replacement?: They remain identical on every set of branches
On a Venn diagram, how do you calculate the probability of an outcome landing in a region?: Divide the number of elements in that region by $n(\mathcal{E})$ , the total in the universal set
What does $P(A \cap B)$ represent?: The probability that an outcome lies in both set A and set B (the intersection)
What does $P(A \cup B)$ represent?: The probability that an outcome lies in set A, set B, or both (the union)
How many sets can Venn diagrams involve at Core level vs Extended?: Core: two sets only; Extended: up to three sets
State the formula for relative frequency.: $\frac{\text{number of successful trials}}{\text{total number of trials}}$
State the formula for expected frequency.: $\text{probability} \times \text{number of trials}$
A coin is flipped 150 times and lands heads 84 times. What is the relative frequency of heads?: $\frac{84}{150} = 0.56$