Compound Probability

Independent Events Involving “And” P(A and B) = P(A) x P(B) Example: Suppose you roll a number cube and flip a coin. What is the probability of rolling a 4 and flipping a heads?

Example: Suppose you roll a number cube and pull a random card from a normal deck. What is the probability of rolling an even number and pulling a face card?

Dependent Events involving “And” Example A: Suppose you have a bag of candy which includes 15 red pieces, 12 blue pieces, and 10 green pieces. What is the probability that the first piece you eat will be green and the second piece you eat will be blue?

Example B: What is the probability that the first and second piece you eat are both red?

Compound Events Involving “OR” Mutually Exclusive Events: Events that cannot occur at the same time. Ex. suppose you want to know the probability of rolling a 2 or a 4 on a number cube. Since a number cube can only show one number at a time ,the events are mutually exclusive . If two events are mutually exclusive, then the probability that either A or B occurs is the sum of their probabilities. P(A or B) = P(A) + P(B)

Example: What is the probability of rolling a 2 or a 4 on a number cube? Example: A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability that it is yellow or green?

Non-Mutually Exclusive Events Involving “Or” When two events, A and B, are non-mutually exclusive, the probability that A or B will occur is: P(A or B) = P(A) + P(B) - P(A and B) Example: In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a girl or an A student?

Example: A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a king or a club?

Dependent Events Involving “OR” Example A: Suppose you have a bag of candy which includes 15 red pieces, 12 blue pieces, and 10 green pieces. What is the probability that the first piece you eat will be green or the second piece you eat will be blue?

Example B: What is the probability that the first piece you eat eat is red or the second piece that you eat is red?