Probability

Probability of an Event A measure of the likelihood that an event will occur. Example: What is the probability of selecting a heart from a standard deck of cards?

Independent Events Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. When two events, A and B, are independent, the probability of both occurring is: Ex: What is the probability of selecting an ace from a standard deck and rolling a 3 on a standard 6-sided die? Selecting a card does not affect rolling a die. These events are independent. “AND” = Multiplication Rule

Dependent Events Two events are dependent if the occurrence of first event (A) affects the probability of the second event (B) from occurring. When two events, A and B, are dependent, the probability of both occurring is: Ex: Two cards are chosen at random from a deck of 52 cards without replacement. What is the probability of choosing two aces? Since the 1 st ace is not put back in the deck, there is one less Ace and one less total card. The probability of selecting a 2 nd ace has changed. These events are dependent. “AND” still equals Multiplication Rule without replacement Fancy way of writing: Probability of B if you know A occurred. OR Ace AND an Ace. (Multiplication Rule) two aces

Addition Rule Given events A and B, the probability that A or B will occur can be found using the formula below : Ex: Sam's closet contains blue and green shirts. He has eight blue shirts, and seven green shirts. Five of the blue shirts have stripes, and four of the green shirts have stripes. What is the probability that Sam randomly chooses a shirt that is blue or has stripes ? “OR” = Addition Rule