Unit 6: Probability- Lesson 7

Unit 6: Probability

Lesson 7 - Independent Events

Independent Events

• When one event does not affect the outcome of the other event, the events are independent.

• Ex: Toss a coin twice, the first toss has no affect on the second toss.

Probability of an Independent Event

• The probability of two independent events can be determined by multiplying the probabilities of the first event by the probability of the second event

• P(A and B) = P(A) x P(B)

• Think: This happened and this happened.

Probability of rolling a 5 and spinning a red on the spinner.

• P(5) = 1/6

• P(Red) = 1/5

• P(5 AND Red) = 1/6 x 1/5 = 1/30

Multiple Choice

Event: Rolling a Number Cube and Spinning the Spinner in the image.

Determine the probability of rolling a AND spinning the spinner and landing on Red.

• 1/6

• 1/5

• 1/15

• 1/30

Determining the Outcomes

• You can use:

• lists

• tree diagrams

• tables

• multiplication

Multiple Choice

You select a letter from the letter tiles A,B,G, and E, and spin a Spinner with 3 equally divided sections A,B, and C. What is the probability that both events will be a vowel.

• 1 / 4

• 1 / 6

• 1 / 7

• 1 / 12

Multiple Choice

The spinner shown and a number cube are used in a game. What is the probability of a player NOT spinning blue and then rolling a 3 or 4?

• P(Not Blue) = 4/5

  P(3 or 4) = 1/6 + 1/6 = 1/3

  P(Not Blue AND 3 or 4) = 4/5 + 1/3 = 17/15

• P(Not Blue) = 4/5

  P(3 or 4) = 1/6 + 1/6 = 1/3

  P(Not Blue AND 3 or 4) = 4/5 x 1/3 = 4/15

• P(Not Blue) = 1/5

  P(3 or 4) = 1/6 + 1/6 = 1/3

  P(Not Blue AND 3 or 4) = 1/5 + 1/3 = 8/15

Multiple Choice

Event: Drawing 2 marbles at Random

Probability ( Yellow and Blue) = ?

• P(Yellow) = 3/12 = 1/4

  P(Blue) = 4/12 = 1/3

  P(Y & B) = 1/4 + 1/3 = 7/12

• P(Yellow) = 3/12 = 1/4

  P(Blue) = 4/12 = 1/3

  P(Y & B) = 1/4 x 1/3 = 1/12

• P(Yellow) = 3/12 = 1/3

  P(Blue) = 4/12 = 1/3

  P(Y & B) = 1/3 + 1/3 = 2/2

Multiple Choice

The word "AND" in probability means . . .

• addition

• subtraction

• multiplication

• division

Multiple Select

A game requires players to roll 2 number cubes to move the game piece. The cube is labeled 1-6 [one number per face of the cube]. What is the probability of rolling a 2 or a 4 on the first number cube and then rolling a 5 on the second? Select all possible methods.

• P(2 or 4) = 1/6 + 1/6 = 2/6 = 1/3

  P(5) = 1/6

  P(2 or 4 AND 5) = 1/3 x 1/6 = 1/18

• Favorable Sample Space: {(2,5) and (4,5)}

  Total Favorable = 2

  Total Outcomes = 36

  Favorable/Total = 2/36 = 1/18

• P(2 or 4) = 1/6 x 1/6 = 1/12

  P(5) = 1/6

  P(2 or 4 AND 5) = 1/12 + 1/6 = 3/12 = 1/4

Poll

How do you feel after this lesson?