This binomial distribution worksheet and solved example problem with step by step calculation helps user to understand how the values are being used in the formula to calculate discrete probability of number of successes and failures in n number of independent trials or experiments. P(x) is the probability of x successes occur in the n number of events, p is the probability of success and q is the probability of failure often denoted by q = (1 - p).
Binomial Distribution Formula Where,
n = Number of events
x = Number of success
p = Probability
Example Problem 2 A lot contains 1 percent of defective items. What would be the number(n) of items in a random sample so that the probability of finding at least one defective in it, is at least 0.95?
Solution: Success = finding a defective item
X = number of success
P = probability of success = 1/100= 0.01
q = 1-p = 0.99