Problem 2 (Probability table, conditional probability and independence). Beth flies from Miami to Pittsburgh with a 25-m

[answerhappygod]

Problem 2 Probability Table Conditional Probability And Independence Beth Flies From Miami To Pittsburgh With A 25 M 1 (444.45 KiB) Viewed 166 times

Problem 2 (Probability table, conditional probability and independence). Beth flies from Miami to Pittsburgh with a 25-minute layover in Atlanta. If Beth misses her connection, she will have to spend the night in Atlanta. The probability that Beth's flight from Miami to Atlanta arrives on time is 0.7; the probability that it is delayed is 0.3. If Beth arrives on time in Atlanta, the probability that she makes the connection to Pittsburgh is 1, If she is delayed arriving in Atlanta, the probability that she makes her connection to Pittsburgh is 0.4. (2.1) Easy. Consider the following events: 0 = Flight from Miami arrives ON TIME in Atlanta; D = Flight from Miami is DELAYED arriving in Atlanta; M = Beth MAKES the connection in Atlanta, N = Beth does NOT make the connection and therefore spends the night in Atlanta. Fill in the probability table. MN 0 0.7 0.3 D 1 (2.2) Easy. What is the probability that Beth's flight is delayed arriving in Atlanta AND she makes her connection to Pittsburgh. (2.3) Easy. What is the probability that Beth makes her connection in Atlanta? If Beth arrives on time in Altanta, the probability that her luggage makes the connection with her is 0.8. If Beth's flight is delayed arriving in Atlanta, the probability that both Beth and her luggage make the connection is 0.1. (2.4) Moderate. What is the probability that both Beth and her luggage make it to Pittsburgh on her scheduled flight? (2.5) Moderate. Are the events 0 = "Beth's flight from Miami arrives ON TIME in Atlanta" and L = "Beth makes the connection and her LUGGAGE is there at her arrival in Pittsburgh" statistically independent? (2.6) Challenging. Given that Beth made it to Pittsburgh on her scheduled flight, what is the probability that her luggage is there at her arrival in Pittsburgh? (2.7) Challenging. Beth made it to Pittsburgh on her scheduled flight and her luggage was not there at her arrival. What is the probability that Beth's flight from Miami was delayed arriving in Atlanta? (Hint: Let K = "Beth made it to Pittsburgh on her scheduled flight and her luggage was not there at her arrival". You need to compute P(DK). Note that M = LUK and that L and K are mutually exclusive.]