A probability distribution table links every outcome of a statistical experiment with the probability of the event occurring. The result of an experiment is listed as a variate , usually written as a capital (for example, X or Y). For instance, if you were to toss a coin 3 times, the possible outcomes are:

TTT, TTH, THT, HTT, THH, HTH, HHT, HHH

You have a 1 out of 8 chance of getting no heads in the least if you throw TTT. The probability is 1/8 or 0.125, a 3/8 or 0.375 chance of throwing one head with TTH, THT, and HTT, a 3/8 or 0.375 chance of throwing two heads with either THH, HTH, or HHT, and a 1/8 or .125 chance of getting three heads.

The following table lists the variate (the number of heads) along side the probability of you getting either 0,1,2, or 3 heads.

Probabilities are written as numbers between 0 and 1; 0 means there’s no chance in the least, while 1 means the event is for certain. The sum of all probabilities for an experiment is usually 1, because if you conduct and experiment, something is sure to happen! For the coin toss example, 0.125+0.375+0.375+0.125=1.

More complex probability distribution tables

Of course, not all probability tables are quite as simple as this one. For instance, the Bernoulli distribution table lists common probabilities for values of n (the number of trials in an experiment).Probability Distribution Table: what’s it?

Statistics Definitions > Probability Distribution Table

What is a Probability Distribution Table?

A probability distribution table links every outcome of a statistical experiment with the probability of the event occurring. The result of an experiment is listed as a variate , usually written as a capital (for example, X or Y). For instance, if you were to toss a coin 3 times, the possible outcomes are:

TTT, TTH, THT, HTT, THH, HTH, HHT, HHH

You have a 1 out of 8 chance of getting no heads in the least if you throw TTT. The probability is 1/8 or 0.125, a 3/8 or 0.375 chance of throwing one head with TTH, THT, and HTT, a 3/8 or 0.375 chance of throwing two heads with either THH, HTH, or HHT, and a 1/8 or .125 chance of getting three heads.

The following table lists the variate (the number of heads) along side the probability of you getting either 0,1,2, or 3 heads.

Number of heads (X) Probability P(X)

0 0.125

1 0.375

2 0.375

3 0.125

Probabilities are written as numbers between 0 and 1; 0 means there’s no chance in the least, while 1 means the event is for certain. The sum of all probabilities for an experiment is usually 1, because if you conduct and experiment, something is sure to happen! For the coin toss example, 0.125+0.375+0.375+0.125=1.

## More complex probability distribution tables

Of course, not all probability tables are quite as simple as this one. For instance , the Bernoulli distribution table lists common probabilities for values of n (the number of trials in an experiment).

## Probability distribution table

The more times an experiment is run, the more possible outcomes there are. The above table shows probabilities for n=8, and as you’ll see — the table is sort of large. However, what this suggests is that you simply , as an experimenter, don’t need to undergo the difficulty of writing out all of the possible outcomes (like the coin toss outcomes of TTT, TTH, THT, HTT, THH, HTH, HHT, HHH) for every experiment you run. Instead, you’ll ask a probability distribution table that matches your experiment.