Probability

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• 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) = 2

• 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?

1.P(Country CD) =

2.P(A movie sound track CD) =

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• 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 BlueGreen Green

1. What is P(heads and blue) =

2. P(heads and green) = 4

• Another example of independent events:– On a six-sided die:

1. P(2 and 3) =

2. P(3, 4, and 5) =

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) = 6

• 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) =

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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) =

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Now you try:

• Find the probability of drawing each of the following letters in MATHEMATICAL if the letters are not replaced:

1.P(A and then T) =

2. P(a vowel and then a vowel) =

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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?

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TOD:

1. Explain the difference between independent and dependent events.

2. Pick one of the following:a. Write an example of two independent events.b. 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)

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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:

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.

Soda Regular DietOrange 3 4Lemon-lime 7 6

• 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.

1.What are the odds of drawing a green marble from the bag?

2.Yellow?

Another example• Find the odds in favor of each outcome if a

die is rolled:1. A number greater than 5

2. A number less than 4

3. A multiple of 2 or a 1

4. 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.

1.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?

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• 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.

1.What are the odds against selecting a heart or what are the odds of not selecting a heart?

2.What are the odds against selecting an ace or what are the odds of not selecting an ace?

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Now you try:

• You have a bag full of M&Ms. There are 12 red, 10 blue, 8 green, 6 yellow, and 4 orange.

1.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?

HomeworkRed Workbook

p. 87(2-22 evens)

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Example: The spinner below is spun.

1 6

5

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2

1. P(yellow or 2) =

2. P(red or 5) =

3. P(3 or blue) =