1. What are the chances of that happening?

2. What is probability? The mathematical expression of the chances that a particular event or outcome will happen. Laws of probability apply only to “random chance events” ( meaning that chance is the only factor affecting the outcome). Could laws of probability be used to determine the chances of you getting an A in this class. Why or why not? What are some examples of random chance events? Rolling dice, picking a certain card from a deck, winning a raffle etc.

3. Basic Law of Probability Probability of a = # of desired outcomes particular outcome # of possible outcomes So the probability of getting heads while flipping a coin is… 1 (head) 2 ( possible sides)

4. How is probability expressed? Often as a fraction: ½ Or the decimal equivalent:.5 Or a percent: 50% (You should be able to easily go back and forth between these three.)

5. 2. The Product Rule Probability of 2 or more chance events ALL occurring is equal to the PRODUCT of their individual probabilities. Example: What is the probability of tossing heads on a penny and heads on a nickel? prob. heads on penny = 1/2 prob. heads on nickel = 1/2 Probability of heads on both: 1/2 x 1/2 = 1/4 CLUE: Key word: “and” (sometimes “both”) Remember: “and” = multiply

6. TIP: If there is MORE THAN ONE WAY to get a desired outcome : a. calculate probabilities for each of the ways. b. ADD all the probabilities for the different ways together. Example: You can win the raffle with either a blue ticket (1/100 chance) or a red ticket (3/100 chance). Your chances of winning are 1/100 + 3/100 = 4/100 CLUE: Key words “either/or” Remember: “or” = add

7. Practice problems 1.What is the probability of rolling 2 dice and getting a 5 on both of them? 2. What is the probability of rolling a die a getting either a 6 or a 3? 3. If you toss two coins together 80 times, how many times would you expect to get tails on both coins? 4. If you toss two coins together 80 times, how many times would you expect to get one tails and one heads? 5. If you toss a coin 4 times, what is the probability of getting heads all 4 times?

8. Practice problems 6. What is the probability of drawing a heart from a deck of cards? 7. What is the probability of drawing a 7 from a deck of cards? 8. What is the probability of drawing a 7 of hearts from a deck of cards? 9. What is the probability of drawing a Queen from a deck of cards and then an 8? (assume you put the first card back in) 10. What is the probability of drawing an Ace or a Jack from one card draw?