Basic Concepts of Discrete Probability
... Probability Measure • Let us consider an event of interest A as the set of outcomes ak. • Let a real function m(ak ) be the probability measure of the outcome ak. • The probability measure of an event is defined as the sum of the probability measures associated with all the outcomes ak of that even ...
... Probability Measure • Let us consider an event of interest A as the set of outcomes ak. • Let a real function m(ak ) be the probability measure of the outcome ak. • The probability measure of an event is defined as the sum of the probability measures associated with all the outcomes ak of that even ...
Example 3, Pg. 253, #7
... First consider whether the two events are mutually exclusive. By definition, one must exclude the other. Ask yourself: if the first card is an ace does that mean it can’t be a diamond? If it does then the two events are mutually exclusive. Since a deck of cards contains an ace that is a diamond, our ...
... First consider whether the two events are mutually exclusive. By definition, one must exclude the other. Ask yourself: if the first card is an ace does that mean it can’t be a diamond? If it does then the two events are mutually exclusive. Since a deck of cards contains an ace that is a diamond, our ...
Chapter 3 More about Discrete Random Variables
... pY |X (yj |xi ) := P(Y = yj |X = xi ) P(X = xi , Y = yj ) pXY (xi , yj ) ...
... pY |X (yj |xi ) := P(Y = yj |X = xi ) P(X = xi , Y = yj ) pXY (xi , yj ) ...
Hitting 10
... [Note: If I'm using this problem in class, it works well to put the class into groups of two to play this game a few times, and collect some data. We see if the game really seems to be fair, and we get a "hands-on" feel for the analysis.] 3. Here’s a generalization of 2. Suppose that Annie and Bill ...
... [Note: If I'm using this problem in class, it works well to put the class into groups of two to play this game a few times, and collect some data. We see if the game really seems to be fair, and we get a "hands-on" feel for the analysis.] 3. Here’s a generalization of 2. Suppose that Annie and Bill ...
A ∩ B
... When events A and B are independent, we can simplify the general multiplication rule since P(B| A) = P(B). Multiplication rule for independent events If A and B are independent events, then the probability that A and B both occur is P(A ∩ B) = P(A) • P(B) ...
... When events A and B are independent, we can simplify the general multiplication rule since P(B| A) = P(B). Multiplication rule for independent events If A and B are independent events, then the probability that A and B both occur is P(A ∩ B) = P(A) • P(B) ...
13.1 The Basics of Probability Theory
... compartments. Thirty-six of the compartments are numbered 1 to 36 with half of them colored red and the other half black. The remaining 2 compartments are green and numbered 0 and 00. A small ball is placed on the spinning wheel and when the wheel stops, the ball rests in one of the compartments. Wh ...
... compartments. Thirty-six of the compartments are numbered 1 to 36 with half of them colored red and the other half black. The remaining 2 compartments are green and numbered 0 and 00. A small ball is placed on the spinning wheel and when the wheel stops, the ball rests in one of the compartments. Wh ...
