T-Maze Each day, mice are put into a T-maze (a maze shaped like a “T”; Fig. 7). In this maze, they have the choice of turning to the left (are rewarded with cheese) or to the right (receive cheese along with mild shock). After the first day, their decision whether to turn left or right is influenced by what happened on the previous day. Of those that go to the left on a certain day, 90% go to the left on the next day and 10% go to the right. Of those that go to the right on a certain day, 70% go to the left on the next day and 30% go to the right.
Figure 7
a. Set up the
b. Compute the second power of the matrix in part (a).
c. Suppose that, on the first day (day 0), 50% go to the left and 50% go to the right. So, the initial distribution is given by the column matrix
d. Make a guess as to the percentage of mice that will go to the left after 50 days. (Do not compute.)
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
EBK FINITE MATHEMATICS & ITS APPLICATIO
- Conditional probability If 40 of the population have completed college, and 85 of college graduates are registered to vote, what percent of the population are both college graduates and registered voters?arrow_forwardRoulette American roulette is a game in which a wheel turns on a spindle and is divided into 38 pockets. Thirty-six of the pockets are numbered 1-36, of which half are red and half are black. Two of the pockets are green and are numbered 0 and 00 (see figure). The dealer spins the wheel and a small ball in opposite directions. As the ball slows to a stop, it has an equal probability of landing in any of the numbered pockets. (a) Find the probability of landing in the number 00 pocket. (b) Find the probability of landing in a red pocket. (c) Find the probability of landing in a green pocket or a black pocket. (d) Find the probability of landing in the number 14 pocket on two consecutive spins. (e) Find the probability of landing in a red pocket on three consecutive spins.arrow_forwardForming an Experimental Group To conduct an experiment, researchers randomly select five students from a class of 20. How many different groups of five students are possible?arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning