K 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(A and B) Use the information below to find the probability that a flight arrives on time given that it P(B|A)= P(A) departed on time. The probability that an airplane flight departs on time is 0.91. The probability that a flight arrives on time is 0.86. The probability that a flight departs and arrives on time is 0.81. The probability that a flight arrives on time given that it departed on time is (Round to the nearest thousandth as needed.)

Determine whether the events A and B are independent. P(Ac) = 0.3, P(Bc) = 0.1, P(A ∩ B) = 0.63 Yes or No

Let A and B be two events such that the probability of B is 0.5 and the probability of both is 0.2. Find the probability of A given that B occurs.

A conditional Probability: P(A | B) is asking what is the probability we get event A if we know that event B occurred. A useful formula: P (A | B) = ||| P(A and B) P(B) Or: P(A | B) = (remaining # of ways to get A) / (remaining number of possible outcomes) A bag has 5 red balls, 7 green balls, and 8 purple balls. Two balls are going to be selected. After the first ball is drawn it is NOT returned to the bag. Find the probability the second is a red ball if you know the first chosen is a red ball. If A = event a red ball is selected: P(A|A) = ?

Determine if each event is independent or dependent.  Then find the probability. When Luis plays Jose on his video game, the probability that Luis will win is 4/7.  What is the probability that he will win the next four games?                                                                                                                                          _______________

Insurance: An insurance company sells a 1-year term life insurance policy to an 80-year-old woman. The woman pays a premium of $4000. If she dies within 1 year, the company will pay $53,000 to her beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 80-year-old woman will be alive 1 year later is 0.9259. Let X be the profit made by the insurance company. Part: 0 / 2 Part 1 of 2 (a) Find the probability distribution. The probability distribution is X P(x) 4000 ☑

Determine if each event is independent or dependent.  Then find the probability.   According to one meteorologist, on a randomly chosen day in January the probability of snow in Buffalo is 65%.  Given that it snows in Buffalo, the probability of snow in Toronto is 75%.  What is the probability that on a randomly  chosen day in January, it snows in both Buffalo and Toronto?                                                                                                                                   ___________________

Insurance: An insurance company sells a 1-year term life insurance policy to an 84-year-old woman. The woman pays a premium of $1400. If she dies within 1 year, the company will pay $46,000 to her beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 84-year-old woman will be alive 1 year later is 0.9714. Let X be the profit made by the insurance company. Part: 0 / 2 Part 1 of 2 (a) Find the probability distribution. The probability distribution is x 1400 X P(x)