A gambler at a casino decided to play a certain card game. The probability that the gambler will win money at the game is 0.45. The probability that he will lose money is 0.55. True or false: According to the law of large numbers, in the long run the gambler will end up with negative winnings when playing against the house.
TrueAccording to the law of large numbers, as the sample size increases, the sample mean gets closer and closer to μ. Thus, the law of large numbers guarantees the house a profit resulting in a loss for a gambler in the long run.
True.
The law of large numbers states that as the number of trials of an experiment increases, the experimental probability of an event will approach the theoretical probability. This means that if the gambler plays the game over a large number of trials, then the ratio of wins to losses will approach the theoretical probability of winning (0.45).
However, since the theoretical probability of winning is less than 0.5, it means that in the long run, the gambler is more likely to end up with negative winnings. This is because even if the gambler wins some games, the losses will eventually outweigh the wins as the number of trials grows large.
Therefore, we can conclude that according to the law of large numbers, in the long run, the gambler will end up with negative winnings when playing against the house.
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