P(0) Probability of exactly 0 successes
If using a calculator, you can enter and into a binomial probability distribution function (PDF). If doing this by hand, apply the binomial probability formula:
The binomial coefficient, is defined by
The full binomial probability formula with the binomial coefficient is
Where n is the number of trials, p is the probability if success on a single trial, and X is the number of successes. Substituting in values for this problem, and
Evaluting the expression, we have
If we apply the binomial probability formula, or a calculator's binomial probability distribution (PDF) function, to all possible values of X for 6 trials, we can construct a complete binomial distribution table. The sum of the probabilities in this table will always be 1. The complete binomial distribution table for this problem, with and 6 trials is:
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