## Applied Mathematics## Probability Theory |

## What are independent events in probability? |

In probability theory, events are independent if the probability that they occur is equal to the product (multiply together) of the probabilities of either two or more individual events. (This is also often called statistical independence.) In addition, the occurrence of one of the events can give no information about whether or not the other event(s) will occur; that is, the events have no influence on each other.

For example, two events, *A* and *B,* are independent if the probability of both occurring equals the product of their probabilities, or P (*A*) | P(*B*) (the symbol “|” is often used to depict the product of the events in probability theory). One good example involves playing cards. If we wanted to know the probability of two people each drawing a king of diamonds (two independent events), it would be defined as *A =* 1/52 (the probability that one person will draw a king of diamonds) and *B =* 1/52 (the probability that the other person will draw a king of diamonds, assuming the first person puts the first drawn card back into the deck). Substituting the numbers into the equation, the result is: 1/52 | 1/52 = 0.00037, or a slight chance that both people will draw the king of diamonds from the deck.