Question 10.6.P.2: Explain why entry (6, 3) of A is .5p1.

Linear Algebra and Its Applications

Explain why entry (6, 3) of A is $.5 p_{1}$ .

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For entry (6, 3) of A, the probability of a transition from state 2:k to state 13:k is required. Suppose that only second base is occupied and that the batter does not make an out. To leave players on first base and on third base, the batter must get to first base, and the player on second base must advance to third. The desired outcome occurs when the batter hits a single, but the runner from second base will then stop at third base with probability .5. The $(6,3) \text {-entry is thus } .5 p_{1}$ .

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