# Disjoint events that are mutually exclusive both

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Disjoint – events that are mutually exclusive (both cannot occur at the same time) Key Concepts: Chance behavior is unpredictable in the short run, but has a regular and predictable pattern in the long run Probability Rules Any probability is a number between 0 and 1 The sum of the probabilities of all possible outcomes must equal 1 If two events have no outcomes in common, the probability that one or the other occurs is the sum of their individual probabilities The probability that an event does not occur is 1 minus the probability that the event does occur Probability of certainty is 1 Probability of impossibility is 0

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Chapter 6: Probability and Simulation: The Study of Randomness Example 1: Using the application on your calculator flip a coin 1 time and record the results? Now flip it 50 times and record the results. Now flip it 200 times and record the results. (Use the right and left arrow keys to get frequency counts from the graph) Number of Rolls Heads Tails 1 51 251 Example 2: Draw a Venn diagram to illustrate the following probability problem: what is the probability of getting a 5 on two consecutive rolls of the dice? Example 3: Given a survey with 4 “yes or no” type questions, list all possible outcomes using a tree diagram. Divide them into events (number of yes answers) regardless of order. Example 4: How many different dinner combinations can we have if you have a choice of 3 appetizers, 2 salads, 4 entrees, and 5 deserts? Example 5: What are your odds of drawing two hearts (from a normal 52-card deck)? a) If you draw a card and replace it and then draw another b) If you draw two cards (without replacing)?
Chapter 6: Probability and Simulation: The Study of Randomness Example 1: Identify the problems with each of the following a) P(A) = .35, P(B) = .40, and P(C) = .35 b) P(E) = .20, P(F) = .50, P(G) = .25 c) P(A) = 1.2, P(B) = .20, and P(C) = .15 d) P(A) = .25, P(B) = -.20, and P(C) = .95 Example 2: A card is chosen at random from a normal deck. What is the probability of choosing? a) a king or a queen b) a face card or a 2 Example 3: What is the probability of rolling two dice and getting something other than a 5? Example 4: Find the following probabilities: A) P(rolling 2 sixes in a row) = ?? B) P(rolling 5 sixes in a row) = ?? Example 5: A card is chosen at random from a normal deck. What is the probability of choosing? a) a king or a jack b) a king and a queen c) a king and red card d) a face card and a heart Example 6: P(rolling a least one six in three rolls) = ?? Example 7: There are two traffic lights on the route used by Pikup Andropov to go from home to work. Let E denote the event that Pikup must stop at the first light and F in a similar manner for the second light. Suppose that P(E) = .4 and P(F) = . 3 and P(E and F) = .15. What is the probability that he: a) must stop for at least one light?

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