Law of Large Numbers Essay Sample
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Law of Large Numbers Essay Sample
Jacob B. Bernoulli founded the Law of Large Numbers (ocw. mit. edu, 2005). This law is also called the law of averages. According to Bernoulli, the more the number of observations the more accurate the probability would be for a given event. To further describe the law, quoted from the probability theory, the law of large number means: “If the probability of a given outcome to an event is P and the event is repeated N times, then the larger N becomes, so the likelihood increases that the closer, in proportion, will be the occurrence of the given outcome to N*P. In a toss coin, the expected probability is 50% because there are only 2 outcomes in a toss coin: heads or tails.
If a coin is tossed 10 times and the outcome is 6 heads and 4 tails this means that the probability to get heads would be 60% for the ten trials. However, if the coin is repeatedly, the chances of getting heads would go near the expected probability of 50%. It may not be exactly 50% but the computation would definitely show a value that is near the expected probability. This could be either 45% to 55% of the probability of getting heads.
Another explanation for the toss coin is first 100 spins resulted to 60 heads and 40 tails imagine that the next 100 spins result in 56 heads and 44 tails. As a correction the percentage of heads has now dropped from 60 per cent to 58 per cent. The number of heads is now 32 as compared to tails, where there were only 20 before. The ‘law of averages’ follows 12 more tosses to head. If the third hundred tosses result in 50 heads and 50 tails, the ‘corrective’ is still proceeding, as there are now 166 heads in 300 tosses, down to 55-33 per cent, but the tails backer is still 32 tosses behind.
Based on the shown example. As the number of tosses gets larger, the probability is that the percentage of heads or tails thrown gets nearer to 50%, but that the difference between the actual number of heads or tails thrown and the number representing 50% gets larger. In flipping a coin the expected result would be 500 times. It may seem that if a coin is flipped 1,000 times, a person would expect to get heads 500 times. However, this may not be the case.
Probability is chance so this does not mean that it would be definite. The law of large number states that the more trial there is the nearer the probability would be to 50% but this does not guarantee a flat 50% outcome. In another scenario, if a person tossed a coin and gets tails three times in a row, the chances of getting heads on the next toss would not be greater than 50%. Simple explanation is that the probability of tossing a coin is 50% and this would not change.
The outcome of getting heads for the next tosses is independent from the last previous tosses of the coin. Even if a person gets heads 10 times in a row, the probability of getting tails on the next still does not change it would still be 50%. The Law of Large Numbers can be misleading to some however, a person must always consider that each trial is independent of each other. Independent in a sense that a success or a failure of the previous trials does not affect the probability of the next trials to come.