Joint Probability

The joint probability of two events A and B is defined as the probability of the intersection of A and B. It is denoted as P(A ∩ B) and can be calculated using the following formula:

\begin{equation} P(A \cap B) = P(B|A)P(A) = P(A|B)P(B) \end{equation}

where P(B|A) and P(A|B) are the conditional probabilities of B given A and A given B, respectively. P(A) and P(B) are the probabilities of A and B, respectively.

This formula can be interpreted in two ways. The first equation says that the joint probability of A and B is equal to the probability of B given A multiplied by the probability of A. This is useful when the probability of A is known and we want to calculate the probability of both A and B occurring.

The second equation says that the joint probability of A and B is equal to the probability of A given B multiplied by the probability of B. This is useful when the probability of B is known and we want to calculate the probability of both A and B occurring.

Overall, the joint probability formula is a fundamental concept in probability theory and is used to calculate the probability of multiple events occurring together.

Question:

In a deck of 52 cards, find the probability of a card that is red in color, and contains the number 6.

Solution:

P(Six and Red) = 2/52

Explanation:

There are two red color Sixes are present in a deck of 52, the 6 of hearts and the 6 of diamonds.