9. A lottery has a winner every day. The winning number is chosen randomly each day, and the probability of winning on any one day is 0.03. Alice plans to buy a lottery ticket every day for 500 days, and Bob plans to buy a ticket every day for 5,000 days. Which of the following is the best assessment of how the law of large numbers applies to this situation? (A) Alice will probably have a higher propor- tion of wins than Bob. (B) Bob will probably have a higher propor- tion of wins than Alice. (C) The difference between Alice's propor-

9. A lottery has a winner every day. The winning number is chosen randomly each day, and the probability of winning on any one day is 0.03. Alice plans to buy a lottery ticket every day for 500 days, and Bob plans to buy a ticket every day for 5,000 days. Which of the following is the best assessment of how the law of large numbers applies to this situation? (A) Alice will probably have a higher propor- tion of wins than Bob. (B) Bob will probably have a higher propor- tion of wins than Alice. (C) The difference between Alice's propor-

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

9. A lottery has a winner every day. The winning
number is chosen randomly each day, and the
probability of winning on any one day is 0.03.
Alice plans to buy a lottery ticket every day for
500 days, and Bob plans to buy a ticket every
day for 5,000 days. Which of the following is
the best assessment of how the law of large
numbers applies to this situation?
(A) Alice will probably have a higher propor-
tion of wins than Bob.
(B) Bob will probably have a higher propor-
tion of wins than Alice.
(C) The difference between Alice's propor-
tion of wins and Bob's proportion of
wins will probably be close to 0.03.
(D) Alice will probably have a proportion of
wins closer to 0.03 than Bob.
(E) Bob will probably have a proportion of
wins closer to 0.03 than Alice.

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Example 7.40: You set out on a walk with three possible locations, denoted locations 1, 2 and 3. The probabilities of travelling from a specified location to the next are given by Solution. If you know that you started in location 3, what is the probability that you end up at location 1 after two time periods? Using the above equation, we get To solve this we use the equation Xn+1 = AXn. Given that you began in location 3, the initial state vector is and subsequently Exercise X₁ = AX0 Probability = A = = X₂ = AX₁ 0.5 0.2 0.4 0.4 0.6 0.1 0.1 0.2 0.5 = Xo 0 0.5 0.2 0.4 0.4 0.6 0.1 0.2 0.5 0.1 ][ Therefore the probability of ending up in location 1 after two time periods is 0.42. 0.5 0.2 0.4 0.4 0.6 0.1 0.1 0.2 0.5 1 0.4 0.1 = 0.5 0.4 0.1 0.5 = 0.42 0.27 0.31 Refer to the example above. If you know that you started in location 2, what is the probability that you will end up at location 1 after one time period?