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Answer:
Law of large number states that if an experiment is repeated independently many times, the expected value should be close to the average. In law of large numbers, as the sample size grows, the mean will get closer to the total number.
In this case, we are told that the mean payoff from a $1 bet is 94.7 cents. Since, the mean payoff is 94.7 cents, the long run average on each lost bet will be 5.3 cents (100-94.7). From the law of large numbers, it can be expected that in the long run a gambler will lose a total of 5.3 cents multiplied by the total the number of bets placed. It means that, if a gambler places a bet on red 800 times, expecting that after 800 spins he loses all 800 times we i.e 800×5.3cents = $42.49
the law of large numbers tells us that when a gambler makes very many bets on red in the given question he will be in the lost.
Given-
Total slots in roulette wheel is 38 units.
Total black slots are 18.
Total red slots are 18.
Total green slots are 2.
Total return on $1 bet on red slot is $2.
If the gambler makes the bet on red slots of the roulette wheel in a large number the average value of experiment reach to the mean of that experiment.
Here the odds the ball landing on the red or black slot is 18/38 and the odds of the ball landing on the green slot is 2/38.
Now the mean payoff from $1 bet is 18/38 or 94.7 cents. It means he gets only 94.7 percent of his total money if play on a large number on red. To understand this suppose he plays 1000 times on red in which on an average the number of times he win is,
[tex]P_b=\dfrac{18}{38} \times 1000[/tex]
[tex]P_b=473.68[/tex]
Hence, the law of large numbers tells us that when a gambler makes very many bets on red in the given question he will be in the lost.
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