MAT 120 Section 3.2 Conditional Probability and the Multiplication Rule

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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.


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