Determine if the events "used cream" and "used sugar" are independent.

Question

One morning 30 employees were in the company cafeteria. Fifteen used cream in their coffee, 20 used sugar and 10 used both.

Answer 1

Let us consider Event A as the employee used cream.

Let us consider Event B as the employee used sugar.

There are 30 employees in company cafeteria out of which 15 used cream in their coffee, 20 for used sugar in their coffee and 10 used both.

Probability of employees who used cream is 15 employees out of 30 employees P(A) = 15/30 = 0.5

Probability of employees who used sugar is 20 employees out of 30 employees P(B) = 20/30 = 0.66

Probability of employees who used both cream and sugar is 10 employees out of 30 employees =10/30=0.33

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

P(A)*P(B) = 0.5 * 0.66 = 0.33

Therefore which means events are independent.

Therefore the events "employees used cream" and "employees used sugar" are independent events.