Probability Simple and Compound

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) = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 P(rolling an even number) = P(5) = P(rolling an odd number)= P(not prime) =

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

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) =

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.

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) ⋅ 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) ⋅ P(B following A) Example: without replacing the first card, choosing an ace and then a king from a deck of cards

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.

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 =

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 =

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 =

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 =