Probability models > Yes/no probabilities
1234Yes/no probabilities

Theory

A particular type of chance experiment is found in situations where:

  • there is a sequence of identical trials;

  • each of these trials has only two possible outcomes: "yes" or "no" (a particular property is observed in the trial or not);

  • the chance of outcome "yes" is the same in each trial, and therefore the chance of outcome "no" is the same in each trial as well;

This is then called a binomial experiment.
In the corresponding tree diagram the probabilities are the same in every layer.

If the chance of success ("yes") is p in each trial, then the chance of failure ("no") is q = 1 - p .
When you repeat the trial n times then the probability of observing a "yes" k times is:

P ( X = k ) = ( n k ) p k q n k

The expression ( n k ) gives you the number of possible sequences in which you will observe k successes ("yes") and n - k failures ("no"). This is the number of combinations of k in n .

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