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- 1. Two coins are tossed. What is the conditional probability that the two heads result, given that there is at least one head? 2. Given P(A) = 0.60, P(B) = 0.40, P(A∩B) = 0.24, Find (i) P(A|B) (ii) P(B|A) (iii) P(AUB) (iv) what is the relationship between A and B? 3. From a well shuffled pack of 52 playing cards, 2 cards are drawn in a succession with out replacement. Find the probability that first card is King and the second is Queen.??Suppose that vehicles taking a particular freeway exit can turn right (R), or turn left.(L). Consider observing the direction for each of three successive vehicles. Which of the following sets represents the event B that at least two of the three vehicles turn left? Select one or more: O a. {(R,R,R),(R,R,L),(R,L,R),(L,R,R)} O b. { (R,L,L),(L,L,L),(R,R,L)} O C. {(L,L,R), (L,R,L), (R,L,L), (L,L,L)} O d. None of these O e. {(R,R,R),(L,L,L),(L,R,L)} O f. {(R,R),(L,R),(R,L)}
- Given the following fictitious data 40% of all undergraduates at XYZ University are from Florida and60% from out of state. 22% are freshmen, and 78% are not. Out of all freshmen, 36% are from Florida,and 64% from out of state. Determine the probability a randomly selected XYZ University undergraduate:Suggestion: Make a tree diagram with the first branches being freshmen or not.a) is from Florida and a freshman. b) is from Florida and not a freshman.c) is from out of state and not a freshman. d) is a freshman given the student is from Florida.Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.Suppose a survey of 300 Ryerson University students was conducted to determine their smoking habits. How many students engaged in only one of the three behaviours? Use the information to below to help formulate your answer. • 90 smoke cigarettes, 18 use e- cigarettes, and 76 use marijuana • 62 smoke cigarettes and use marijuana • 8 smoke cigarettes and use e- cigarettes • 12 smoke marijuana and use e- cigarettes • 6 engage in all three behaviours
- 5. A group of n people stand in a line. On the count of three, each of them simultaneously chooses to look either left or right (with equal probability): at one of their neighbors. Let X be the number of pairs of adjacent people that end up facing each other. (For example, if n = 5 and the random facings are "Left, Left, Right, Left, Right" then only the 3rd and 4th people face each other.) (a) Find the expected value E[X]. (b) Find Pr[X=0]. (c) Assuming n is even, find the maximum possible value of X, and the probability that X is equal to that value.1. The admissions office of a private university released the following admission data for the preceding academic year:from a pool of 3900 male applicants, 40% were accepted by the university and 40% of those males subsequently enrolled.Additionally, from a pool of 3600 female applicants, 45% were accepted by the university and 40% of those femalessubsequently enrolled.Make a tree diagram for this situation.What is the probability that:a) a male applicant will be accepted by and subsequently will enroll in the university?b) a student who applies for admission will be accepted by the university?c) a student who applies for admission will be accepted by the university and subsequently will enroll?