 # Formal Probability. The sum of probabilities for all possible outcomes of a trial must equal 1. Example: Flipping a Coin S = {Heads, Tails} P(H) = 0.5.

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Formal Probability

The sum of probabilities for all possible outcomes of a trial must equal 1. Example: Flipping a Coin S = {Heads, Tails} P(H) = 0.5 P(T) = 0.5 P(H)+P(T) = 0.5+0.5 = 1 or P(S) = 1

The complement of an event consists of outcomes that are not in the event.

1)If A = rolling an even on a 6-sided die, what is the complement of A? 2)If B = flipping a coin and landing on Tails, what is the complement of B? 3)If C = passing your class, what is the complement of C?

Data was collected on a stoplight which determined that the light is green 35% of the time. What is the probability that if you approached the stoplight it would not be green? P(not green) = 1 – P(green) = 1 - 0.35 = 0.65

Events are independent if one does not affect the other. Example of Independent Events Rolling a 5 and then rolling a 6: the probability of rolling a 6 on the second roll is not affected by whether or not the first roll was a 5 Example of Dependent Events Drawing a King on the first draw and then a King on the second draw: the probability of drawing a King on the second draw depends on if a King was drawn already removed from the deck

Disjoint (often called mutually exclusive ) events have no outcomes in common. Disjoint Events: A = drawing a face card B = drawing a 2 Not Disjoint Events: A = drawing a face card B = drawing a diamond

Suppose that 40% of cars in your area are manufactured in the United States, 30% in Japan, 10% in Germany, and 20% in other countries. If cars are selected at random, find the probability that: 1)A car is not U.S. made 2)It is made in Japan or Germany 3)You see two in a row from Japan 1-P(made in U.S.) = 1 – 0.4 = 0.6 P(G) + P(J) = 0.3 + 0.1 = 0.4

Suppose that 40% of cars in your area are manufactured in the United States, 30% in Japan, 10% in Germany, and 20% in other countries. If cars are selected at random, find the probability that: 1)None of three cars came from Germany 2)At least one of three cars is U.S. made 3)The first Japanese car is the 4 th one chosen

Law of Averages – NO! A couple just had their 5 th child, another boy! All 5 of their children have been boys. They thought that after having 4 boys, the 5 th child HAD to be a girl because of the law of averages! The Law of Averages is not a real thing! Every child has a 50% chance of being genetically male and a 50% chance of being genetically female, regardless of the gender of the children that came before.

Today’s Assignment:  Worksheet  Add to HW #9 page 338 #6-8, 19-24, 31, 32

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