Mary and John are playing the following game: They have a three-card deck marked with the numbers 1, 2, and 3 and a spinner with the numbers 1, 2, and 3 on it. The game begins by dealing the cards out so that the dealer gets one card and the other person gets two. A move in the game consists of a spin of the spinner. The person having the card with the number that comes up on the spinner hands that card to the other person. The game ends when someone has all the cards.

(a) Set up the transition matrix for this absorbing Markov chain, where the states correspond to the number of cards that Mary has.
(b) Find the fundamental matrix.
(c) On the average, how many moves will the game last?
(d) If Mary deals, what is the probability that John will win the game?

understand that i don't know the answers

will someone answer his question

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both graphs increase on their domain

neither graph has a y-intercept

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the following points can be visualized easily from the graph

the above table 1 will calculate the population size (n) after a certain length of time (t). all you need to do is plug in the initial population number (no), the growth rate (r) and the length of time (t). the constant (e) is already entered into the equation. it stands for the base of the natural logarithms (approximately 2.71828). growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. for humans, population growth rate is based on one year. if a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent.

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