Textbooks from seven different subjects are to be arranged randomly in a bookshelf. What is the probability that in the arrangement exactly one textbook separates the textbooks for math and english?
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- You own 21 CDs. You want to randomly arrange 8 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? The probability that the CDs are in alphabetical order isProblem 4: A finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine is a binary value; it can only be 0 or 1. The probability of the input being 0 is 0.4. (a) Plot the state transition diagram and find the transition probability matrix given that: . When the input is 1 the machine moves to the state above the current state (2 is above 1, 3 is above 2, 1 is above 3). . When the input is 0 the machine moves to the state below the current state (1 is below 2, 2 is below 3, 3 is below 1). These are the only two possible transitions. (b) If the process starts in state 1 (Xo = 1), what is the probability that it will be in state 2 after 3 transitions (X3 = 2)? (c) If we know that the process starts in state 3 (Xo = 3), what are the 3 state probabilities after two transitions (that is, at time k = 2)?A class consisting of 4 graduate students and 12 undergraduate students is randomly divided into four groups of 4. What is the probability that each group includes a graduate student?
- an after-school club consists of 10 juniors and 7 seniors. If 4 students are chosen at random to represent the club at a school fair, what is the probability that at least one student from each class level is selected?A class consists of 18 boys and 16 girls. The teacher will randomly choose three students to be on a special committee. What is the probability that more girls are on the committee than boys?Jean puts 12 books on a shelf in random order. Three are by the same author. What is the probability that those 3 books will be next to each other?
- A bag contains 9 RED beads, 4 BLUE beads, and 8 GREEN beads. If a single bead is picked at random, what is the probability that the bead is BLUE or GREEN?The report is open numbers are 1121, 1170, 744, 1353, and 83 and the number from Brooklyn are 1170, 2706, and 48. What is the probability that the report is open and comes from Brooklyn?If Luis has 8 pairs of socks (4 white, two black, one blue, and one red), what is the probability that he randomly chooses two pairs of white socks to wear on consecutive days?
- A golf ball is selected at random from a golf bag. If the golf bag contains 4 green balls, 7 red balls, and 7 brown balls, find the probability of the following event. The golf ball is green or red?Four hundred fifty of the six thousand students at Ocean State College like math, three thousand five-hundred like English, and three hundred like both. What is the probability that one student, chosen at random, likes math or English?A group of six students is chosen at random from a list of five maths students and four psychology students. What is the probability that four maths students and two psychology students are chosen?