John plans to gamble until he has $4 or until he has $0, whichever comes first.
ID: 3022143 • Letter: J
Question
John plans to gamble until he has $4 or until he has $0, whichever comes first. He starts with either $1, $2, or $3. In each bet he will win $1 with probability 0.6 and lose $1 with probability 0.4.
- Find the absorbing state probabilities.
- The expected value of a random variable can be found by multiplying the value of every outcome by its probability and adding the results. Compute the expected gain (or loss) for each of the following situations:
The gambler begins with $1
The gambler begins with $2
The gambler begins with $3
Explanation / Answer
Probability Assignment
John plans to gamble until he has $4 or until he has $0, whichever comes first. He starts with$1, $2, or $3. In each bet he will win $1 with probability 0.6 and lose $1 with probability 0.4.
- Find the absorbing state probabilities.
- The expected value of a random variable can be found by multiplying the value of every outcome by its probability and adding the results. Compute the expected gain (or loss) for each of the following situations:
The gambler begins with $1
The probability for win is given as 0.6 and probability for lose is given as 0.4.
Expected gain = $1*0.6 - $1*0.4 = 0.6 – 0.4 = $0.2
The gambler begins with $2
Expected gain = $2*0.6 - $2*0.4 = 1.2 – 0.8 = $0.4
The gambler begins with $3
Expected gain = $3*0.6 - $3*0.4 = 1.8 – 1.2 = $0.6
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