brown law firm collected data on the transportation choices of its employees for their morning commute. the…
brown law firm collected data on the transportation choices of its employees for their morning commute. the table shows the percentages of the type of transportation of the male and female employees. consider the following events: a: the employee is male. b: the employee is female. c: the employee takes public transportation. d: the employee takes his/her own transportation. e: the employee takes some other method of transportation. which two events are independent? a and c a and d b and d b and e
Answer
Explanation:
Step1: Recall independence formula
Two events (X) and (Y) are independent if (P(X\cap Y)=P(X)\times P(Y)).
Step2: Calculate probabilities for each option - A and C
(P(A)=\frac{36}{60} = 0.6), (P(C)=\frac{20}{60}=\frac{1}{3}), (P(A\cap C)=\frac{12}{60}= 0.2). And (P(A)\times P(C)=0.6\times\frac{1}{3}=0.2). So (P(A\cap C) = P(A)\times P(C)).
Step3: Calculate probabilities for A and D
(P(A)=\frac{36}{60}=0.6), (P(D)=\frac{30}{60} = 0.5), (P(A\cap D)=\frac{20}{60}=\frac{1}{3}\approx0.33), (P(A)\times P(D)=0.6\times0.5 = 0.3\neq P(A\cap D)).
Step4: Calculate probabilities for B and D
(P(B)=\frac{24}{60}=0.4), (P(D)=\frac{30}{60}=0.5), (P(B\cap D)=\frac{10}{60}=\frac{1}{6}\approx0.17), (P(B)\times P(D)=0.4\times0.5 = 0.2\neq P(B\cap D)).
Step5: Calculate probabilities for B and E
(P(B)=\frac{24}{60}=0.4), (P(E)=\frac{10}{60}=\frac{1}{6}), (P(B\cap E)=\frac{6}{60}=0.1), (P(B)\times P(E)=0.4\times\frac{1}{6}\approx0.067\neq P(B\cap E)).
Answer:
A. The employee is male and C. The employee takes public transportation.