Probability

12. Based on historical data, an insurance company estimates that a particular customer has a 2.4% likelihood of having an accident in the next year, with the average insurance payout being $1500. If the company charges this customer an annual premium of $100, what is the company's expected value of this insurance policy?

What is the empirical probability that a randomly selected female superhero will have telepathy?s

Question 2 (1 point) A spinner is broken into sections labeled 1 to 40. What is the probability that, on your next spin, that you will spin a number less than 3?

What is the empirical probability that a randomly selected superhero will be able to fly?

What is the empirical probability that a randomly selected superhero will have super strength?

3. [6] Consider the experiment of throwing two dice. (a) [3] Find the probability of the event that the second dice shows a larger number of dots than the first one. (b) [3] Find the probability of the even that the second dice shows a larger number of dots than the first one given that the sum of the two dice is not greater than 4.

9. [10] A computer generates hexadecimal characters (e.g. 0000, 0001, 0010, etc.). Let \X" be the integer value corresponding to a hex character. Suppose that the four binary digits in the character are independent and each is equally likely to be \0" or \1". (a) [2] Describe the underlying space of this random experiment and specify the probabilities of its elementary events. (b) [3] Show the mapping fromS to Sx. (c) [5] Find the probabilities for the various values ox.

2. Of fifty students surveyed, twenty-five played volleyball thirty-three played basketball and four played neither sport. a) How many students played both sports? b.) Complete the Venn-Diagram. c) Find the probabilities: i) P ( play both sports) ii) P (play Volleyball only) (iii) P (play neither) iv) P (play Voleyball or basketball)

3. The executive of the Manitoba Association of Mathematics Teachers consists of 3 women and 2 men. In how many ways can a president and secretary be chosen if: (a) the president must be female and the secretary male? (b) The president must be male and the secretary female? (c) The president and secretary are of opposite sex?

2. Suppose that 70% of students attend a 9:00 am course. Of these students, 80% have a course at 10:00. Suppose 60% of students have a course at 10:00. Let A= Event that student has a course at 9:00, and B= Event that student has a course at 10:00 a. Find the probability a student has a class at 9:00. b. Find the probability a student has a class at 10:00. c. Find the probability a student has a class at 10:00, given that they have a class at 9:00. d. Find the probability that a student has a class at 9:00 and a class at 10:00. e. Is having a class at 9:00 and having a class at 10:00 independent? Justify an answer. f. Is having a class at 9:00 and having a class at 10:00 mutually exclusive? Justify answer. g. What is the probability a student has a class at 9:00, given that they have a class at 10:00? h. What is the probability a student has a class at 9:00 or a class at 10:00.