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JT360 | Free Listen.. Compass I M oodle M Gmail M U of I Mail in Linkedin Handshake D UIUC Enterprise N Netflix Thesaurus Need Help?Read ItWatch Master 0.55/1.11 points | Previous Answers TanFin 12 9.3.026.CMI My Notes Ask Your Tear Diane has decided to play the following game of chance. She places a $1 bet on each repeated play of the game in which the probability of her winning $1 is.8. She has further decided to continue playing the game until she has either accumulated a total of $3 or has lost all her money What is the probability that Diane will eventually leave the game a winner if she started with a capital of $1? of $22 capital of $1 16/21 capital of $2 35/42 Master It 0.75/1.12 points 1 Previous Answers TanFin 12 9.3.030·CMI. My Notes Ask Your Teach The registrar of a law school has compiled the following statistics on the progress of the school's students working toward the LLB degree: Of the first-year students in a particular year, 88% successfully complete their course of studies and move on to the second year, whereas 12% drop out of the program; of the second-year students in a particular year, 92% go on to the third year, whereas 8% drop out of the program: of the third- year students in a particular year, 98% go on to graduate at the end of the year, whereas 2% drop out of the program 1 (a) Construct the transition matrix associated with the Markov process. (Label your matrix using this order: Drop out, Graduate, First- Year, Second-Year, Third-Year) LiveExplanation / Answer
Let W= Win & L = Loose in a bet chance
If she started with:
P(W) = 0.8
P(L) = 0.2
a) $1
WW + WLWW + WLWLWW+WLWLWLWW ...... =
= 0.8^2 * (1 + 0.8*0.2 + (0.8*0.2)^2 + ..)
= 0.64 * 1/(1 - 0.16)
= 0.64/0.84
= 16/21
b) $2
W + LWW+ LWLWW+ LWLWLWW + LWLWLWLWW ......
= 0.8(1 + 0.8*0.2 + (0.8*0.2)^2 + . ...)
= 0.8 * 1 /(1 - 0.16)
= 0.8/0.84
= 20/21
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