In this situation, our data would follow the following joint probabilities:

To calculate the joint probability of the coincidence occurring in any one minute we multiply the two separate probabilities.

In the following soft clustering example, the reference vector contains sample categories and the joint probability is assumed known.

However, the two tests are not completely redundant; as a result the joint probability of their rejection is less than α.

After the solution attempt, the principle behind the joint probability of two independent events will be explained, using the chosen example.

Teachers may then use the other examples in order to deepen the understanding of joint probabilities, for example by using worked examples.

Consequently, estimates of joint or conditional probabilities are both continuous and differentiable.

We use the shorthand notation to denote the joint probability of by .

Often it is inconvenient to achieve the perfect joint probability of due to rounding issues.

The cool result was joint probabilities greater than and less than one.