In the teacher's pencil box, 7 out of 20 pencils have an eraser, and 9 out of 20 are mechanical pencils. 4 pencils are both mechanical and have an eraser on them. What is the probability that Ava chooses a pencil at random from the box and gets a. Mechanical pencil with an eraser? b. Either a mechanical pencil or a pencil with a good eraser?. -A student is taking two courses, Statistics and Economics. The probability that a student will pass a statistics course is .83, and the probability of passing the economics course is 0.66. The probability of passing both is 0.62. a. What is the probability of passing at least one? b. What is the probability of failing both? . What is the probability of either passing a Statistics course or an Economics course but not both? Mr. and Mrs. Peanuts are retired and live in a Texas retirement community. Suppose the probability that a retired man will live another 10 years is 0.60. The probability that a retired woman will live another 10 years is 0.70. a. What is the probability that both Mr. and Mrs. Peanuts will be alive 10 years from now? b. What is the probability that in 10 years, Mr. Peanut is not living and Mrs. Peanut will be living? c. What is the probability that in 10 years, both will not be living? d. What is the probability that in 10 years, at least one will be living?