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Pre-Algebra

The probability of overlapping and mutually exclusive events is identified and founded.

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After completing this tutorial, you will be able to complete the following:

- After completing this Activity Object, learners will be able to:
- Identify overlapping or mutually exclusive events.
- Find the probability of mutually exclusive events.
- Find the probability of overlapping events.

The concept of probability

Probability is the measure of how likely it is that an event will occur.

P(E) (read P of E) stands for the probability of event E

n(E) stands for the number of ways E can happen

n(U) stands for the number of elements in the sample space U

For example,

When rolling a die, what are the probabilities of rolling a 4 and not rolling a 4?

Not rolling a 4 is more likely to occur.

Compound events

If two or more events are combined with the word and or the word or, they are called compound events. Mutually exclusive and overlapping events are compound events. Each of them includes more than one events combined with the word or.

Mutually exclusive events

Two or more events are said to be mutually exclusive events (disjoint events) if they cannot occur at the same time. Such events have no outcomes in common. If two events A and B are mutually exclusive, then the probability of the occurrence of A or B is the sum of their individual probabilities:

For example,

A six-sided die is rolled once.

Event A: Rolling a number greater than 4,

Event B: Rolling a number less than 4,

Events A and B are mutually exclusive because they can't occur at the same time.

Overlapping events

Two or more events are said to be overlapping events if one or more event occurs at the same time.

For two overlapping events A and B, the probability that either of the events occurs is the sum of the probabilities of the events, minus the probability that both events occur:

For example,

A six-sided die is rolled once.

Event A: rolling an odd number,

Event B: rolling a number higher than 4,

Events A and B are overlapping because one or more event occurs at the same time, namely 5.

Approximate Time | 25 Minutes |

Pre-requisite Concepts | Students should know the definitions of event, intersection of sets, probability of simple events, union of sets, and more likely. |

Course | Pre-Algebra |

Type of Tutorial | Concept Development |

Key Vocabulary | intersection, mutually exclusive events, outcomes |