Contingency Tables and Probability

a future event that is possible, but cannot be predicted with certainty

• conditional

• contingency

• complement

• disjoint

• non-uniform

all outcomes in the sample space but not in the event

• non-uniform

• disjoint

• overlapping

• contingency

• complement

events that have no outcomes in common

• non-uniform

• disjoint

• overlapping

• contingency

• complement

a probability distribution where all outcomes are equally likely

• uniform

• contingency

• disjoint

• overlapping

• complement

You are asked to calculate: "the probability of randomly selecting a red diamond from a number of colored shapes". Using "R" for red and "D" for diamond, which is the proper set notation for this probability?

You are asked to calculate: "if you randomly select a diamond, what is the probability it is coloured red". Using "R" for red and "D" for diamond, which is the proper set notation for this probability?

You are asked to calculate: "if you randomly select a red shape, what is the probability it is a diamond". Using "R" for red and "D" for diamond, which is the proper set notation for this probability?

You are asked to calculate: "the probability of randomly selecting a red shape or a diamond from a number of colored shapes". Using "R" for red and "D" for diamond, which is the proper set notation for this probability?

Given the data from the contingency table to the left, if you randomly select a yellow shape, what is the probability it is a triangle?

• 20%

• 40%

• 60%

Answer explanation

The phrase "if you randomly select a yellow shape" tells us we are only going to look at the data for yellow shapes.

We are being asked for the probability we select a triangle.

In set notation, we would write: P( T | Y )

We find that there are 2 triangles, so the number of favorable outcomes is 2.

The total number of yellow shapes is 5, so the number of possible outcomes is 5.

The probability of an event is: the number of favorable outcomes divided by the number of possible outcomes.

For this question, the probability is 2/5 which is equal to 40%.

Given the data from the contingency table to the left, if you randomly select a triangle, what is the probability it is a yellow shape?

• 20%

• 40%

• 60%

Answer explanation

The phrase "if you randomly select a triangle" tells us we are only going to look at the data for triangles.

We are being asked for the probability we select a yellow shape.

In set notation, we would write: P( Y | T )

We find that there are 2 triangles, so the number of favorable outcomes is 2.

The total number of triangles is 3, so the number of possible outcomes is 3.

The probability of an event is: the number of favorable outcomes divided by the number of possible outcomes.

For this question, the probability is 2/3.