Probability

Example: A six sided die – 1, 2, 3, 4, 5, 6 Probability – a ratio that tells how likely it is that an event will take place. probability = Example: A six sided die – 1, 2, 3, 4, 5, 6 What is the probability of getting a 2 or P(2)? 1. P(odd number) = 2. P(a number less than 1) = 3. P(a number less than 3) =

Another example: I’ve got 13 CD’s. 6 are rock CD’s, 3 are country CD’s, and 4 are movie sound track CD’s. If I choose a CD at random, what is the probability that I will choose a country CD? P(Country CD) = P(A movie sound track CD) =

Independent events – two or more events in which the outcome of one event does not affect the outcome of the other. Example: I have a coin and a spinner: RED Blue Green Green 1. What is P(heads and blue) = 2. P(heads and green) =

Another example of independent events: On a six-sided die: 1. P(2 and 3) = 2. P(3, 4, and 5) =

Now you try: You have a six-sided die and a spinner 1. P(5 and orange) = 2. P(even number and yellow) = 3. P(3 and black) =

Dependent Events: two or more events in which the outcome of one event does affect the outcome of the other event. Can you think of an example? Example: You are going to draw a card out of a deck of cards. The first one is not replaced. 1. What is P(a king and then a 3) = 2. P(a queen and then a heart) =

Another example of dependent events: In a bag there are 5 red marbles, 2 green marbles, 4 yellow marbles, and 3 blue marbles. Once a marble is drawn, it is not replaced. Find: 1. P(green and then green) = 2. P(red, green, and then a blue) =

Now you try: Find the probability of drawing each of the following letters in MATHEMATICAL if the letters are not replaced: P(A and then T) = 2. P(a vowel and then a vowel) =

Independent or Dependent? 1. Rolling a die twice? 2. Selecting a name from the Greenville phone book and a name from the Greer phone book? 3. As team captain, selecting someone to be on your basketball team and then selecting a second player? 4. Tossing a coin and spinning a spinner? 5. Choosing a card from a deck of cards and then choosing a second card without replacing the first card?

TOD: 1. Explain the difference between independent and dependent events. 2. Pick one of the following: Write an example of two independent events. Write an example of two dependent events 3. What math operation does the word and represent in this statement: P(drawing a king and then a queen)

The chart below lists the number and type of two soft drinks found in a tub filled with ice. Two cans are selected at random. Find the probability of the following: Soda Regular Diet Orange 3 4 Lemon-lime 7 6 1. a diet orange and a regular lemon-lime 2. a regular orange and a regular lemon-lime 3. A diet lemon-lime and a regular lemon-lime 4. a regular orange and a diet lemon-lime.

Odds (in favor) – the ratio of the number of ways the outcome can occur (successes) to the number of ways the outcome cannot occur (failures). odds (in favor) = # of successes : # of failures Example: A bag contains 5 green marbles, 2 yellow marbles, and 3 blue marbles. What are the odds of drawing a green marble from the bag? Yellow?

Another example Find the odds in favor of each outcome if a die is rolled: A number greater than 5 A number less than 4 A multiple of 2 or a 1 Not a 3

Now you try: Example: The door prize at a party with 25 people is given by writing numbers 1 through 25 on the bottom of the paper plates used. What is the probability that an individual had the winning plate? 2. What are the odds of winning a door prize? 3. What are the odds of not winning a door prize?

Odds (against) – the ratio of the numbers of ways the outcome cannot occur (failures) to the number of ways the outcome can occur (successes). odds (against) = # of failures : # of successes **What do you notice about odds in favor and odds against? Let’s look at previous examples

Example: A card is selected at random from a deck of 52 cards. What are the odds against selecting a heart or what are the odds of not selecting a heart? What are the odds against selecting an ace or what are the odds of not selecting an ace?

Now you try: You have a bag full of M&Ms. There are 12 red, 10 blue, 8 green, 6 yellow, and 4 orange. What are the odds of you not randomly pulling out an orange M&M? 2. Not a blue nor a red M&M?

Consider this example: 1. The odds of an event are 2:5. What is the probability of the same event? 2. The odds of an event are 3:7. What is the probability of the same event?

Red Workbook p. 87 (2-22 evens) Homework Red Workbook p. 87 (2-22 evens)

Example: The spinner below is spun. P(yellow or 2) = 2. P(red or 5) = 3. P(3 or blue) = 1 6 2 5 3 4