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PROBABILITY - Conditional Probability Examples - Conditional Probability Of Playing Cards

Calculating Conditional Probability, Conditional Probability Of Playing Cards

Conditional Probability of Dice Rolling. Dice Rolling Probability.

Example 1: Probability of getting the flu given that you have been vaccinated
Example 2: Probability of train arriving on time given that it left on time
Example 3: Probability of students passing the second test given that they were able to pass the first test

Example 4:
Example 5:

Conditional Probability Notation:

P(A | B): Probability of A Given B

Conditional Probability Formula:

P(A | B) = P(A ⋂ B) / P(B)

Conditional Probability Venn Diagram.

What Is Conditional Probability?

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome. Conditional probability is calculated by multiplying the probability of the preceding event by the updated probability of the succeeding, or conditional, event.

For example:

Event A is that it is raining outside, and it has a 0.3 (30%) chance of raining today.
Event B is that you will need to go outside, and that has a probability of 0.5 (50%).

P(A | B) = (0.3 * 0.5)/0.3 = 50%

A conditional probability would look at these two events in relationship to one another, such as the probability that it is both raining and you will need to go outside.

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