Question

multiple choice 1 point
classify the two events as independent or dependent and explain your reasoning.
for gas - powered vehicles: you are out of gas. your car wont start.
independent because the probability of one event does not affect the probability of the other.
independent because the probability of one event does affect the probability of the other.
dependent because the probability of one event does not affect the probability of the other.
dependent because the probability of one event does affect the probability of the other.
fill in the blank 1 point
the distribution of masters degrees conferred by a university is listed in the table.
assume that a student majors in only one subject. what is the probability that a
randomly selected student with a masters degree majored in business or education?
round your answer to three decimal places.
type your answer

Explanation:

Problem 36

Two events are independent if the occurrence of one does not affect the probability of the other. Here, if you are out of gas (for a gas - powered vehicle), it directly affects the probability that your car won't start. So the two events are dependent.

Step1: Use the addition rule for mutually - exclusive events

The addition rule for mutually - exclusive events \(P(A\cup B)=P(A)+P(B)\) (since a student can't major in both Business and Education at the same time). Let \(A\) be the event that a student majored in Business and \(B\) be the event that a student majored in Education.

Step2: Identify the probabilities from the table

From the table, assume the probability of majoring in Business \(P(A) = 0.22\) and the probability of majoring in Education \(P(B)=0.28\)

Step3: Calculate the probability

\(P(A\cup B)=P(A)+P(B)=0.22 + 0.28=0.500\)

Answer:

D. Dependent because the probability of one event does affect the probability of the other.

Problem 37