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It is a probability of between 0.3 and 0.7
As the number of times that the experiment is conducted increases, the experimental probability will near the theoretical probability - unless there is a problem with the theoretical model.
Probability is used to extrapolate the likelihood of a future event, so if you think about it, it's used all the time by everyone everyday. Here are some main applications: - Data Analysis - Quantum Mechanics - Thermodynamics - Meteorology - Social Science - Business ans Finance. The list is near endless.
If you roll the die often enough the probability is near enough 1 so as to make no difference. On a single roll, the probability is 1/2.
If the z value is that great the probability of the event is ridiculously small (or large) and you'd have to act as if it were near enough zero (or 1)