A man plays a gambling game which is close to fair (i.e.,chance he wins any part

Question

A man plays a gambling game which is close to fair (i.e.,chance he wins any particular play is a little less than 0.5, andall plays are independent). After losing 8 plays in a row, hestates "By the law of averages (law of large numbers), my chancesof winning on each play should now increase to compensate for myrun of bad luck, so I should keep gambling another 5 - 10 times asI am destined to win." Do you agree or disagree with this man? Briefly,why? Your answer must use and interpret the WLLN in someway. What I know: WLLN = weak Law of LargeNumbers I disagree with the man, knowing that each play is independentof the play before and the play after it. I do not know how to use the Law of Large Numbers.

Explanation / Answer

There is a famous simulation where a fair coin is tossed 10000times. Basically, the Law of large numbers says that with enoughsimulations, the number of heads/tails would approach theprobability of 1/2. Let's say 4895 heads. which is quite close to1/2. In this case, the situation is similar. So, even though each experiment is independent, in the long rangenumber of heads should be close to number of tails.

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