Question

In a recent survey about appliance ownership, 58.3% of the respondents indicated that they own Maytag appliances, while 23.9% indicated they own both Maytag and GE appliances and 70.7% said they own at least one of the two appliances. Define the events as: M = Owning a Maytag appliance G = Owning a GE appliance [1] What is the probability that a respondent owns a GE appliance? [1] Given that a respondent owns a Maytag appliance, what is the probability that the respondent also owns a GE appliance? [2] Are events "M" and "G" mutually exclusive? Explain, using probabilities. [2] Are the two events "M" and "G" independent? Explain, using probabilities.

Answer 1

Solution: M = Owning a Maytag appliance   G = Owning a GE appliance

Given: P(M)=0.583 P(MG)=0.239 P(MG)=0.707

1] What is the probability that a respondent owns a GE appliance?

Answer: The probability that a respondent owns a GE appliance is calculated as follows.

P(MG)=P(M)+P(G)-P(MG)

0.707=0.583+ P(G) -0.239

P(G)=0.583-0.239-0.707=0.363

2] Given that a respondent owns a Maytag appliance, what is the probability that the respondent also owns a GE appliance?

P(G/M)=P(MG)/P(M)=0.239/0.583=0.4099

3] Are events "M" and "G" mutually exclusive? Explain, using probabilities.

The condition for two events to be mutually exclusive is P(MG)0.

In this case P(MG)=0.239, so events M and G are not mutually exclusive.

4] Are the two events "M" and "G" independent? Explain, using probabilities.

The condition for two events to be independent is P(MG)P(M)*P(G).

In this case P(MG)=0.583*0.363=0.2116, which is not equal to zero, so the two events are not independent.