MAT 120 Section 3.2 Conditional Probability and the Multiplication Rule
List an example of two events that are independent. Choose the correct answer below. A. Not putting money in a parking meter and getting a parking ticket. B. A father having hazel eyes and a daughter having hazel eyes. C. Rolling a die twice. D. Selecting a queen from a standard deck, not replacing it, and then selecting a queen from the deck.
ANSWER: C. Rolling a die twice.
What does the notation P(B|A) mean? Choose the correct answer below. A. The probability of event A occurring, given that event B has occurred. B. The probability of event B occurring, divided by the probability of event A occurring. C. The probability of event B occurring, given that event A has occurred. D. The probability of both event A and event B occurring.
ANSWER: C. The probability of event B occurring, given that event A has occurred. A conditional probability is the probability of an event occurring, given that another event has already occurred. The conditional probability of event B occurring, given that event A has occurred, is denoted by P(B|A) and is read as "probability of B, given A."
List an example of two events that are dependent. Choose the correct answer below. A. Selecting a ball numbered 1 through 12 from a bin, replacing it, and then selecting a second numbered ball from the bin. B. Tossing a coin and getting a head, and then rolling a six-sided die and obtaining a 6. C. Rolling a die twice. D. Drawing one card from a standard deck, not replacing it, and then selecting another card.
ANSWER: D. Drawing one card from a standard deck, not replacing it, and then selecting another card. When drawing two cards (without replacement) from a standard deck, the outcome of the second draw is dependent on the outcome of the first draw.
Determine whether the following statement is true or false. If it is false, rewrite it as a true statement. If two events are independent, P(A|B)=P(B). Choose the correct answer below. A. False; if events A and B are independent, then P(B|A) = P(A). B. False; if events A and B are independent, then P(A and B) = 0. C. True D. False; if events A and B are independent, then P(A and B) = P(A) x P(B).
ANSWER: D. False; if events A and B are independent, then P(A and B) = P(A) x P(B). Two events are independent if the occurrence of one of the events does not affect the probability of the occurrence of the other event. Two events A and B are independent if P(B|A)=P(B) or if P(A|B)=P(A).
By rewriting the formula for the multiplication rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B|A) = P(A and B) / P(A). Use the information below to find the probability that a flight departed on time given that it arrives on time. The probability that an airplane flight departs on time is 0.89. The probability that a flight arrives on time is 0.87. The probability that a flight departs and arrives on time is 0.84. What is the probability that a flight departed on time given that it arrives on time?
ANSWER: The probability that a flight departed on time given that it arrives on time is 0.966.
