MT221 Final study guide(2024)

a. Are the events the selected participants is “ daytime” and “evening” mutually exclusive? Explain b. Are the events the selected participant is “preschool” and “levels” mutually exclusive? Explain c. Are the events the selected participant is “daytime” and “preschool” mutually exclusive? Explain d. Find P (preschool). e. Find P (daytime) f. Find P ( not levels) g. Find P ( preschool or evening)  h. Find P ( preschool and daytime) i. Find P ( daytime/ levels) j. Find P (adult and diving/ evening) 45) Determine whether each of the following pairs of events is independent: a. Rolling a pair of dice and observing a “1” on the first die and a “1” on the second die b. Drawing a “spade” from a regular deck of playing cards and then drawing another “spade” from the same deck without replacing the first card c. Same as part b except the first card is returned to the deck without replacing the first card d. Owning a red automobile and having blonde hair e. Owning a red automobile and having a flat tire today f. Studying for an exam and passing the exam 46) Suppose that P (A) = 0.3, P (B)=0.4, and P (A and B) =0.20 a. What is P (A/B) ? b. What is P (B/A)? c. Are A and B independent? 47) One student is selected at random from a group of 200 students known to consist of 140 full-time (80 female and 60 male) students and 60 part-time (40 female and 20 male) students. Event A is “the student selected is full time,” and event C is “the student selected is female.” a. Are events A and C independent? Justify your answer. b. Find the probability P( A and C)  48) You have applied for two scholarships: a merit scholarship (M) and an athletic scholarship (A). Assume the probability that you receive the athletic scholarship is 0.25, the probability that you receive both scholarships is 0.15, and the probability that you get at least one of the scholarship is 0.37. Use a Venn diagram to answer these questions: A. What is the probability that you receive the merit scholarship? B. What is the probability that you do not receive either of the two scholarships? C. What is the probability that you receive the merit scholarship given that you have been awarded the merit scholarship? D. What is the probability that you receive the athletic scholarship, given that you have been awarded the merit scholarship? E. Are the events “receiving an athletic scholarship” and “receiving a merit scholarship” independent events? Explain. 49 Consider the set of integers 1,2,3,4, and 5. A. One integer is selected at random. What is the probability that it is odd? B. Two integers are selected at random (one at a time with replacement so that each of the five is available for a second selection). Find the probability that neither is odd; exactly one of them is odd; both are odd. 50) A box contains 25 parts, of which 3 are defective and 22 are nondefective. If 2 parts are selected without replacement, find the following probabilities: A P(both are defective) B. P (exactly one is defective) C. P (neither is defective) 51) a. Express ( x ) = 16, for x= 1, 2, 3, 4, 5, 6, in distribution form. B. Construct a histogram of the probability distribution P( x )= 16, for x= 1, 2, 3, 4, 5, 6. c. Describe the shape of the histogram in part b 52) a. Explain how the various values of x in a probability distribution form a set of mutually exclusive events b. Explain how the various values of x in a probability distribution form a set of “ all-inclusive” events. 53) Test the following function to determine whether it is a probability function. If it is nit, try to make it into a probability function. S(x) =6-x-736, for x= 2, 3, 4, 5, 6, 7...11, 12 a. List the distribution of probabilities and sketch a histogram.