College Math

College Math Study Guide

player glances to see it is a red face card. Now what is the probability that the card drawn by the second player is a king card? In this case, event A has already taken place, and we must find the probability of event B, the conditional probability will be denoted as P (B|A). ( | ) = ( ∩ ) ( ) In this case, n(A∩B) = number of elements when card is red and king = king of diamond and king of hearts = 2 P(A∩B) = 2/52 n(A) = 26 P(A) = 26/52 ( | ) = 2/52 26/52 = 0.0769 Many times while solving the conditional probability, drawing a Venn diagrams helps to simplify and understand the problem. For instance, in the above case, let us consider the following diagram:

The green portion of the diagram shows all elements or probability for set A, while lemon portion shows that for set B. The middle portion, greenish yellow color shows the elements for the intersection between set A and set B. For the independent events , the conditional probability can be found as follows:

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