Determine if the events "lettrered in a band" and "in honor society are independent".

Question

In a group of 100 college freshmen, 25 lettered in band, 20 were in the honor society and 5 lettered in band and were in the honor society.

Answer 1

Let us consider Event A as the lettered in band.

Let us consider Event B as the Honor Society.

There are 100 people in college out of which 25 are selected for lettered in band and 20 for honor society.

Probability of selecting 25 members out of 100 people is P(A) = 25/100 = 0.25

Probability of selecting 20 members out of 100 people is P(B) = 20/100 = 0.20

Probability of selecting people for both lettered in band and honor society is = 5/100 = 0.05

Two events A and B are said to be independent even when

P(A)*P(B) = 0.25 * 0.20 = 0.05

Therefore which means events are independent.

Therefore the events "lettered in band" and "honor society" are independent events.