Probability of Compound Events

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Presentation transcript:

Probability of Compound Events

Compound Events Made up of two or more events. Example: the probability that a flight will be on time & your luggage will arrive. Create your own compound event.

Independent Events The outcome of one event does NOT affect the outcome of the other. Equation: P(A and B) = P(A) x P(B) Symbol A n B Example 1 : A bag contains 6 black marbles, 9 blue marbles, 4 yellow marbles, and 2 green marbles. A marble is selected, replaced, and a second marble is selected. Find the probability of selecting a black marble, then a yellow marble.

Example 2: P(blue, green) Example 3: P(not black, blue)

Dependent Events The outcome of one event affects the outcome of another event. Equation: P(A and B) = P(A) x P(B following A) Example 4 : A bag contains 6 black marbles, 9 blue marbles, 4 yellow marbles, and 2 green marbles. A marble is selected, then a second marble is selected. Find the probability of selecting a black marble, then a yellow marble.

Example 5: P(blue, green) Example 6: P(not black or blue, blue)

Complement of a Set The set of all objects that do NOT belong to the given set. Example: The probability of drawing a heart & the probability of NOT drawing a heart. Create your own complement. The sum of these probabilities is ALWAYS 1 whole or 100%.

CARDS Total number of cards in a deck? ______ How many suits? _____ Name them. How many cards are in each suit? _____ How many cards of each face? _____ How many different face cards? Name them. How many of each color? _____

Mutually Exclusive Events Events that can NOT occur at the same time. Example: the probability of drawing a heart or a diamond. Equation: P(A or B) = P(A) + P(B) Symbol A u B Example 7: A die is being rolled. Find the probability of rolling a 3 or 5.

Example 8: P(at least 4) Example 9: P(less than 3)

Not Mutually Exclusive Events that CAN occur at the same time. Example: the probability of being on the honor roll, in the SADD club, or being both on the honor roll & in the club. Equation: P(A or B) = P(A) + P(B) – P(A and B)

Example 10: Of 240 girls, 176 are on the Honor Roll, 48 play sports, and 36 are on the Honor Roll and play sports. What is the probability that a randomly selected student plays sports or is on the Honor Roll? Example 11: Out of 5200 households surveyed, 2107 had a dog, 807 had a cat, and 303 had both a dog and a cat. What is the probability that a randomly selected household has a dog or a cat?

Review Draw a model to describe the following terms. Define each: Mutually Exclusive, Independent, Compound Events, Not Mutually Exclusive, & Dependent.

Circle the sample space What is the proportion of students who live in Currituck & are male? What is the probability that a male student who passes Math II is also in the SADD Club?

Name three different probability models… 1. 2. 3. 4.