I found this cool Binomial Probability Calculator from Stat Trek. Plug in the probability of success, the number of trials and the number of successes, and you get a set of probabilities ranging from exact to cumulative.
Here is one problem to try: In a city, it has been estimated that the probability of drivers not wearing seat belts is 10% and driving under the influence of alcohol is 5%. If the police check five people at random, what is the probability of catching at least one person who has committed at least one offence?
The first step is to estimate the probability of success of a single trial (person). Probability of not wearing a seat belt (SB) or drink and drive (DD) = P(SB U DD) = P(SB) + P(DD) – P(SB & DD) = 0.05 + 0.1 – 0.05 x 0.1 = 0.145. The rest is simple, # trials = 5; # success (x) = 1.
The answer we are looking for is the probability of at least one person committing a crime, which is = P(X >/= x) = 0.543 (the last entry in the results).
Now, try this one: The probability of failure (on demand) for a safety instrument is 1 in 10000. A plant has 1000 such instruments. What is the chance that there is at least one (x = 1) failed instrument? The answer P(X >/= x) = 0.095 or about 10%.
References
Binomial probability calculator: Stat Trek
Binomial Distribution Word Problems: superprof
