1.Mr. Amica walks into ISS and takes 3 students out of the 15 in there to help him in the cafeteria. How many possibilities are there for picking the 3 kids? 2. If he assigns jobs to each student where the first person has trash, the second sweeps, and the third puts up signs, how many possibilities are there now? Warm up

Questions over hw? Textbook p. 349 #1 – 10, 17, 18

Daily Check

GPS Algebra Day 4 UNIT QUESTION: How do you use probability to make plans and predict for the future? Standard: MM1D1, MM1D2, MM1D3 Today’s Question: When do I add or multiply when solving compound probabilities? Standard: MM1D2.a,b.

Practice with Conditional Probability

The table gives the handedness and eyedness of a randomly selected group of 100 people.Right-EyedLeft-Eyed Right-Handed 5731 Left-Handed 66 1.If you randomly select a person from this group, what is the probability of getting a left-handed person?

The table gives the handedness and eyedness of a randomly selected group of 100 people.Right-EyedLeft-Eyed Right-Handed 5731 Left-Handed If you randomly select a person from this group, what is the probability of getting someone who is left-eyed?

The table gives the handedness and eyedness of a randomly selected group of 100 people.Right-EyedLeft-Eyed Right-Handed 5731 Left-Handed If you randomly select a LEFT-HANDED person, what is the probability they are left-eyed?

The table gives the handedness and eyedness of a randomly selected group of 100 people.Right-EyedLeft-Eyed Right-Handed 5731 Left-Handed If you randomly select a LEFT-EYED person, what is the probability they are left-handed?

The chart shows favorite subjects of students based on their gender.MathScienceEnglishSS Male Female What is the probability that a randomly chosen student likes history the most?

The chart shows favorite subjects of students based on their gender.MathScienceEnglishSS Male Female What is the probability that a randomly chosen student is female?

The chart shows favorite subjects of students based on their gender.MathScienceEnglishSS Male Female What is the probability that a randomly chosen student both likes science and is a male?

The chart shows favorite subjects of students based on their gender.MathScienceEnglishSS Male Female What is the probability that a randomly chosen student likes social studies given that they are a female?

A compound event combines two or more events, using the word and or the word or. Compound Event

AND Means you MULTIPLY

OR Means you ADD

Mutually Exclusive vs. Overlapping Events

two or more events cannot occur at the same time They have no common outcomes. Mutually Exclusive

Find the probability of each and ADD: P(A or B) = P(A) + P(B) For Mutually Exclusive Events:

Example 1: Using a standard deck of 52 cards: Find the P(4 or Ace). Mutually Exclusive Events

Example 2: When rolling two dice, what is P(sum of 4 or sum of 5)? Mutually Exclusive Events

Example 3: Find the P(Red Queen or King). Mutually Exclusive Events

events have at least one common outcome. You will have to SUBTRACT out the overlapping amount Overlapping

P(A or B) = P(A) + P(B) – P(A and B) Overlapping Events

Example 4: Find the P(King or Clubs)? Overlapping Events

Example 5: Find the P(female or FL) out of the committee members listed in the table. Overlapping Events FemMale FL84 AL63 GA73

Example 6: When rolling 2 dice, what is the P(even sum or a number greater than 10)? Overlapping Events

Independent Events (with replacement) Two events A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Probability of A and B occurring: P(A and B) = P(A)  P(B)

AND Means you MULTIPLY

Example 1 A coin is tossed and a 6-sided die is rolled. Find P(landing on heads and rolling a 3).

Example 2 A card is chosen at random from a deck of 52 cards. It is then REPLACED and a second card is chosen. Find the P(a jack and an 8).

Example 3 A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. A marble is chosen at random from the jar. After replacing it, a second marble is chosen. Find the P(a green and a yellow).

Example 4 A school survey found that 9 out of 10 students like pizza. If 3 students are chosen at random with replacement, find P(all three students like pizza).

Dependent Events (without replacement) Two events A and B, are dependent if the fact that A occurs affects the probability of B occurring. Not replacing will cause you to subtract from the denominator (and sometimes from the numerator).

Example 5 A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles. A marble is chosen at random from the jar. A second marble is chosen without replacing the first one. Find P(a green and a yellow marble).

Example 6 An aquarium contains 6 gold fish and 4 white fish. You randomly select a fish from the tank, do not replace it, and then randomly select a second fish. Find the P(1 st fish is gold and 2 nd fish is gold).

Example 7 A random sample of parts coming off a machine is done by an inspector. He found that 5 out of 100 parts are bad on average. What is the P(1 st part is bad and 2 nd part is bad) if he doesn’t replace the first?

Conditional Probability A math teacher gave her class two tests. 25% of the class passed both tests and 42% of the class passed the first test. What percent of those who passed the first test also passed the second test? 60%

Conditional Probability A jar contains black and white marbles. Two marbles are chosen without replacement. The probability of selecting a black marble and then a white marble is 0.34, and the probability of selecting a black marble on the first draw is What is the probability of selecting a white marble on the second draw, given that the first marble drawn was black? 72%

Conditional Probability The probability that it is Friday and that a student is absent is Since there are 5 school days in a week, the probability that it is Friday is 0.2. What is the probability that a student is absent given that today is Friday? 15%

Conditional Probability At Kennedy Middle School, the probability that a student takes Technology and Spanish is The probability that a student takes Technology is What is the probability that a student takes Spanish given that the student is taking Technology? 13%

Workbook p. 369 #1 – 6

Mutually exclusive or overlapping? P(A or B) =

Mutually exclusive or overlapping? P(A or B) =

Mutually exclusive or overlapping? P(A or B) =

Mutually exclusive or overlapping? P(A or B) =

Mutually exclusive or overlapping? P(A or B) =

Mutually exclusive or overlapping? P(A or B) =