In a certain town, the probability that a person plays sports is 65%. The probability that aperson is between the ages of 12 and 18 is 40%. The probability that a person plays sportsand is between the ages of 12 and 18 is 25%. Are the events independent? How do youknow?

the events are the same and not independent because sports is 65% which is age 12 when you compare the age 12 and 18 to 65% and 40% they sound they are the same. so since 12 is lower than 18 it still has higher percentage and since 18 is higher it has lower percentage

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MrRoyal MrRoyal · Answer 2 · 2021-12-31T13:27:50+01:00

Events in probability can be dependent or independent.

The events are not independent

Represent the events as follows:

A: A person is between the ages of 12 and 18
B: A person plays sport.

So, we have:

[tex]P(A) = 40\%[/tex]

[tex]P(B) = 65\%[/tex]

[tex]P(A\ and\ B) = 25\%[/tex]

For two events A and B to be independent, then the following equation must be true:

[tex]P(A\ and\ B) = P(A) \times P(B)[/tex]

So, we have:

[tex]P(A\ and\ B) = 40\% \times 65\%[/tex]

[tex]P(A\ and\ B) = 0.26[/tex]

Express as percentage

[tex]P(A\ and\ B) = 26\%[/tex]

By comparison:

[tex]26\% \ne 25\%[/tex]

Hence, the events are not independent