Bernoulli Trials Calculator (Range)
This calculator is similar to the ordinary Bernoulli trials probability calculator. It allows you to calculate probability that the number of successes will fall into a given interval.
For example, what is the probability that there will be between 1 and 3 successes when tossing 5 fair coins?
To answer this question, we have to add the probability that there will be 1 success, to the probability that there will be 2 successes, to the probability that there will be 3 successes.
\[ \binom{5}{1} \times {1 \over 2}^{1} \times {1 \over 2}^{4} + \binom{5}{2} \times {1 \over 2}^{2} \times {1 \over 2}^{3} + \binom{5}{3} \times {1 \over 2}^{3} \times {1 \over 2}^{2} \]
The answer is: \(0.15625 + 0.31250+ 0.31250 = 0.78125\). So there is a near 80% probability that the number of successes will be 1, 2 or 3 in 5 trials.