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First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.

A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.

It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.

Or, of course, it could be a mixture of both.

First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.

A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.

It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.

Or, of course, it could be a mixture of both.

First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.

A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.

It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.

Or, of course, it could be a mixture of both.

First, it is important to note that it is very unlikely that the experimental and theoretical probabilities will agree exactly. As an extreme example, if you toss a coin an odd number of times, the resulting experimental probability cannot possibly be exactly 1/2. It should be easy to see that this remains true even if the coin is tossed googleplex+1 number of times.

A negative difference could be because the number of trials was too small and, with an increased number of trials, the experimental probability would gradually increase towards the theoretical probability.

It is also possible that the theoretical model is wrong. You may have assumed that the coin that was being tossed was fair when it was not. Or there were some factors that you failed to take full account of in your theoretical model.

Or, of course, it could be a mixture of both.

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10y ago

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