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Probability Simple and Compound.

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Presentation on theme: "Probability Simple and Compound."β€” Presentation transcript:

1 Probability Simple and Compound

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3 Probability of Simple Events
Simple Event – one outcome or collection of outcomes Probability – the chance of that event happening Outcome – any one of the possible results of an action P(event) = π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘“π‘Žπ‘£π‘œπ‘Ÿπ‘Žπ‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘  π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘œπ‘ π‘ π‘–π‘π‘™π‘’ π‘œπ‘’π‘‘π‘π‘œπ‘šπ‘’π‘  P(rolling an even number) = P(5) = P(rolling an odd number)= P(not prime) =

4 Probability of Compound Events
Mutually Exclusive - Events that cannot occur at the same time P(5 or 6) = P(3, 4 or 5) = P(even or 3) = Probability of Mutually Exclusive Events P(A or B) = P(A) + P(B) P(rolling a 2 or a 3 on a die) = P(2) + P(3) = 1 3

5 Probability of Compound Events
Mutually Inclusive - Events that cannot occur at the same time P(multiple of 2 or even) = P(less than 5 or odd) = Probability of Inclusive Events P(A or B) = P(A) + P(B) – P(A and B) P(black card or 10) = P(black) + P(10) – P(black and 10) =

6 Example: A card is drawn from a standard deck of playing cards. a. Find the probability of drawing a king or a queen. b. Find the probability of drawing a king or a spade.

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8 Probability of Compound Events
Independent Events- Events that do not affect each other. Made up of two or more simple events. Dependent Events- Events in which the outcome of one will effect the other. Probability of Independent Events Outcome of first event does not affect outcome of second. P(A and B) = P(A) β‹… P(B) Example: rolling a 6 on a die and then rolling a 5 Dependent Events Outcome of first event does affect outcome of second. P(A) β‹… P(B following A) Example: without replacing the first card, choosing an ace and then a king from a deck of cards

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10 Example: Find the probability that you will roll a six and then a five when you roll a die twice. A bag contains 3 red marbles, 2 green marbles, and 4 blue marbles. Two marbles are drawn randomly from the bag and not replaced. Find the probability that both marbles are blue.

11 Probability of Compound Events
Examples- What is the probability of rolling a 6 and a coin landing on heads? Probability of rolling a six = Probability of flipping heads = Probability of both =

12 Probability of Compound Events
Examples- What is the probability of dropping a coin down 12 stairs and it landing heads up on the 5th stair? Probability of flipping heads = Probability of landing of the 5th step = Probability of both =

13 Probability of Compound Events
Examples- There is a bag filled with 10 marbles: 6 red, 1 blue, and 3 green. What is the probability of randomly picking out a red marble then a green marble? Probability of red = Modified prob of green = Probability of both =

14 Probability of Compound Events
Examples- There is a bag filled with 10 marbles: 6 red, 1 blue, and 3 green. What is the probability of picking a red then a red then the blue marbles? Probability of red = Modified prob of red = Modified prob of blue = Probability of all =


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