Examples for

Bernoulli Trials

Bernoulli trials are any sequence of independent, random experiments with exactly two possible outcomes and in which the probabilities of success or failure are respectively the same for each individual trial. The computational power of Wolfram|Alpha enables you to conduct your own Bernoulli trials and calculate the probability for a sequence of trials, any specified outcome of successes and failures, or the number of trials required to find a specific number of successes or failures.
Bernoulli Trials

Investigate the probabilities and waiting times for Bernoulli trials.

Compute probabilities for a sequence of trials:

12 Bernoulli trials

Specify a success probability:

18 trials p=.22

Compute the probability of a specific outcome:

probability of 8 successes in 14 trials with p=.6

Analyze waiting-time probabilities:

number of trials until 15th success
observe 54th success on 189th trial

Find the probability of a run:

streak of 12 successes in 40 trials
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Coin Tosses

Compute the results of any number of coin tosses or specify an outcome and calculate the likelihood of it occurring.

Compute coin-toss probabilities:

32 coin tosses

Compute the probability of a specific outcome:

probability 12 heads 8 tails
fewer than 18 heads in 40 tosses

Compute a waiting-time probability:

probability of 3rd head on 8th flip

Compute the probability of a run:

run of 3 heads in 15 flips
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