Street Routs Figure 1 shows a partial map of the streets in New York City. (Such maps are discussed in Chapter 5.) A tourist starts at point A and selects at random a shortest path to point B. That is, they walk only south and east. Find the probability that
(a) they pass through point C.
(b) they pass through point D.
(c) they pass through point C and point D.
(d) they pass through point C or point D.
Figure 1
Figure 2
Want to see the full answer?
Check out a sample textbook solutionChapter 6 Solutions
Finite Mathematics & Its Applications (12th Edition)
Additional Math Textbook Solutions
Probability and Statistics for Engineers and Scientists
Calculus Volume 2
Finite Mathematics (11th Edition)
Mathematics for the Trades: A Guided Approach (11th Edition) (What's New in Trade Math)
Mathematics for Elementary Teachers with Activities (5th Edition)
A Survey of Mathematics with Applications (10th Edition) - Standalone book
- Roulette 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_forwardCustomer Preference Two movie theatres that show several different movies each night compete for the same audience. Of the people who attend theatre A one night, 10 will attend again the next night and 5 will attend Theatre B the next night. Of the people who attend Theatre B one night, 8 will attend again the next night and 6 will attend Theatre A the next night. Of the people who attend neither theatre one night, 3 will attend Theatre A the next night and 4 will attend Theatre B the next night. Find and interpret the steady state matrix for this situation.arrow_forwardConsumer Preference In a population of 100,000 consumers, there are 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month, a Brand A user has a 20 probability of switching to Brand B and a 5 of not using either brand. A Brand B user has a 15 probability of switching to Brand A and a 10 probability of not using either brand. A nonuser has a 10 probability of purchasing Brand A and a 15 probability of purchasing Brand B. How many people will be in each group a in 1 month, b in 2 months, and c in 18 months?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning