Betsy is going purchase some stock. She is trying to choose between 7 tech stocks (one of which is Microsoft) and 12 industrial stocks (one of which is Bethlehem Steel). (a) If she randomly chooses a stock, what is the probability it will be a tech stock? (b) If she randomly chooses a stock, what is the probability it will be Microsoft? (c) If she decides to choose one of the tech stocks, what then is the conditional probability that it will be Microsoft? (d) If she decides to choose one of the industrial stocks, what is the probability it will be Bethlehem Steel?

Tammy is practicing her basketball free throws. On each attempt, she has a 0.2 chance ofsuccessfully making it. Each attempt is independent of the previous ones. She will keepattempting free throws until she makes a successful one.(a) What is the probability that she will make exactly three attempts?(b) What is the probability that she will make no more than three attempts?(c) What is the probability that she will need to make more than three attempts?(d) Prove, using series from calculus, that the probability that she will ultimately make a successful attempt is 1.

A lonely grandma has 12 black cats, 7 grey cats, and 11 orange cats. She decides to give them all a bath at once. If she closes her eyes and pulls two cats from the bathtub, what is the probability that the first cat will be black and the second cat will be orange? (Don't Hand writing in solution) .

A classroom contains 10 girls and 8 boys. You need to randomly select some of the students for testing. You cannot select the same student twice.(a) What is the probability of randomly selecting a girl?(b) If you randomly selected two students, what is the probability of selecting two boys?(c) You randomly select three students. What is the probability that the third student you select is a girl, given the first two were boys?(d) What is the most likely outcome when randomly choosing two students: selecting two of the same gender (2 boys or 2 girls), or choosing a boy-girl pair? Explain your reasoning.