For the following exercises, assume that there are n ways an event A can happen...Use the Multiplication Principle of counting to explain how many ways event A and B can occur.

For the following exercises, assume that there are n ways an event A can happen, m ways an event B can happen, and that A and B are non-overlapping.

Use the Multiplication Principle of counting to explain how many ways event A and B can occur.

Solutions

Expert Solution

An event A can happen in n ways and another event B can happen in m ways. The events A and B are non-overlapping.

Multiplication Principle

“If one event can occur in m ways and a second event with no common outcomes can occur in n ways after the first event has occurred, then the two events can occur in m × n ways.”

Use the multiplication principle,

Total number of ways event ‘A and B’ can occur will be equal to the product of the number of ways the event A can occur and the number of ways the event B can occur.

That is,

Number of ways event ‘A and B’ can occur = number of ways event A can occur × number of ways event B can occur

As,

The event A can occur in n ways and event B can occur in m ways. Hence the event A and B both simultaneously can occur in n × m ways.

Junaid answered 1 year ago

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