4.2: Probability and Events

Question 1

What is the formal definition of an event in probability theory?

Answer 1

An event is a set of one or more sample space outcomes.

Question 2

Provide an example of an event using the experiment of tossing a fair die.

Answer 2

An example of an event in the experiment of tossing a fair die is the event “at least five spots will show on the upward face of the die.”

This event consists of the sample space outcomes 5 and 6.

Question 3

How is the probability of an event calculated based on sample space outcomes?

Answer 3

The probability of an event is calculated as the sum of the probabilities of the sample space outcomes that correspond to the event.

Question 4

What is a tree diagram

Answer 4

A diagram that depicts an experiment as a sequence of steps and is useful when listing all the sample space outcomes for the experiment.

Question 5

How is the probability of an event calculated when sample space outcomes are equally likely in a finite sample space?

Answer 5

When sample space outcomes are equally likely in a finite sample space, the probability of an event occurring is calculated as the ratio of the number of sample space outcomes that correspond to the event to the total number of sample space outcomes.

Question 6

Why is it essential that sample space outcomes are equally likely to use the mentioned probability calculation method?

Answer 6

The mentioned probability calculation method can only be used when all the sample space outcomes are equally likely.

If the outcomes are not equally likely, using this method may result in incorrect probabilities.