16% of students play basketball. 70% of students live in Murfreesboro. 11% of students play basketball and live in Murfreesboro. Are the events "a randomly selected student plays basketball" and "a randomly selected student lives in Murfreesboro" independent or not?

Question

Ismael

Mathematics

29 November, 13:12

16% of students play basketball. 70% of students live in Murfreesboro. 11% of students play basketball and live in Murfreesboro. Are the events "a randomly selected student plays basketball" and "a randomly selected student lives in Murfreesboro" independent or not?

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Answers (1)

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Johanna Benton · Answer 1

They are independent

Step-by-step explanation:

We have the following events:

* 16% of students play basketball

* 70% of students live in Murfreesboro

They ask us if each of the events are independent of the other, the answer is yes. Since the probability in the first event would be 16/100 and the second event 70/100, and at no time are they affected by each other.

They mention another event that that depends on these two:

* 11% of students play basketball and live in Murfreesboro

(16/100) * (70/100) = 0.112, which is equal to 11.2%, which is approximate to the event they mention.