Simple Probability Diagrams Flashcards

All 20 cards in this deck

What are the steps to list all possible combinations of one item from each of two lists?

e.g. starters Salad (S), Fish (F); mains Pasta (P), Rice (R)

1. Pair the first item of list 1 with every item of list 2: SP, SR
2. Repeat for the next item of list 1: FP, FR
3. Check the count: $2\times2=4$ combinations

What check tells you a completed two-way table is consistent?

The row totals and the column totals both add up to the grand total in the bottom-right corner.

From a completed two-way table, how do you find the probability that a person chosen at random from everyone is a female with short hair?

Number in the 'female, short hair' cell $\div$ grand total.

e.g. $\frac{8}{45}$

True or false? If one of the females is chosen at random from a two-way table, the probability she has short hair is the number of short-haired females divided by the total number of people.

False. Divide by the total number of females, not the grand total.

What is a frequency tree?

A diagram showing how a total splits into groups at each stage, with the frequency (a whole number) written in each circle.

In a frequency tree, what must a pair of branch numbers coming from the same point add up to?

The frequency they came from.

e.g. $22$ males split into $18$ right-handed and $4$ left-handed

What are the steps to complete a frequency tree?

e.g. 50 people, 30 are male, 12 of the males passed

1. Fill in the first pair of branches: $50-30=20$ females
2. Use each given value to find its partner: $30-12=18$ males failed
3. Check every pair adds to the number before it

Using a completed frequency tree, how do you find the probability that an adult chosen at random passed?

Number of adults who passed $\div$ total number of adults.

e.g. $\frac{20}{32}$

On a frequency tree, how do you find the total number who passed altogether?

Add the 'passed' frequencies from every branch.

e.g. $20$ adults $+\ 34$ children $=54$

True or false? You should write probabilities on the branches of a frequency tree.

False. A frequency tree is completed with frequencies (whole numbers); using probabilities loses marks.

What does $A \cap B$ mean?

The intersection: the elements that are in both $A$ and $B$ (the overlap).

What does $A \cup B$ mean?

The union: the elements that are in $A$ or $B$ or both.

What does $A'$ mean?

The complement of $A$: everything in the universal set that is not in $A$.

In set notation, what does $\xi$ (also written $E$) stand for?

The universal set: all the elements being considered, shown by the rectangle round the Venn diagram.

What are the steps to complete a Venn diagram from two lists?

e.g. $\xi=\{1,...,10\}$, $A=\{$multiples of $3\}$, $B=\{$even numbers$\}$

1. Put the elements in both sets in the intersection: $6$
2. Fill each 'only' region: $A$ only $3, 9$; $B$ only $2, 4, 8, 10$
3. Put the elements left over outside both circles: $1, 5, 7$

True or false? If 20 students study French and 8 study both French and German, you write 20 in the 'French only' region.

False. Write $20-8=12$, because the 20 already includes the 8 in the intersection.

What are the steps to find a probability from a completed Venn diagram?

e.g. $A$ only $3$, both $2$, $B$ only $4$, outside $1$; find $P(A\cap B)$

1. Count the elements in the region asked for: $2$
2. Count all the elements in $\xi$: $3+2+4+1=10$
3. Write region $\div$ total: $\frac{2}{10}$

True or false? To find how many elements are in $A \cup B$, add the number in $A$ to the number in $B$.

False. That counts the elements in the intersection twice.

True or false? Elements written outside both circles are left out of the denominator when a number is chosen at random from $\xi$.

False. They are part of the universal set, so they count in the total.

True or false? When listing all the possible combinations of one starter and one main course, 'Salad and Pasta' and 'Pasta and Salad' count as the same single combination.

True. One item is taken from each list, so the order you write the pair in does not make a new combination.