Assume that a procedure yields a binomial distribution with a trial repeated times.

Question

Use either the binomial probability formula (or a technology like Excel or StatDisk) to find the probability of successes given the probability of failure on a single trial.

Answer 1

Park,

To find the probability of k successes in n trials with a probability p of failure on a single trial, you can use the binomial probability formula:

P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))



Where:

1. P(X = k) is the probability of k successes in n trials.
2. (n choose k) is the number of combinations of n items taken k at a time.
3. p is the probability of failure on a single trial.
4. (1-p) is the probability of success on a single trial.

Here's how you can calculate it:

1. Calculate (n choose k): (n choose k) = n! / (k! * (n-k)!)
2. Calculate (p^k): This is the probability of having k failures.
3. Calculate ((1-p)^(n-k)): This is the probability of having n-k successes.
4. Multiply All Three Components: Multiply the three components to get the final probability P(X = k).

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Thank you,

Benjamin M.