Probability of Independent Events

Probability of Independent Events

Math II Honors

Mr. Coleman

Unit 5 - Probability

Lesson Objectives

• Identify events that are independent 

• Understand and apply the Addition Rule 

• Understand and apply the Multiplication Rule 

• Solve problems involving compound probabilities of independent events

Independent Events

Have no influence on one another's outcomes

Multiple Select

Which of the following are independent events?

• Rolling a die and flipping a coin

• Drawing two cards from the top of a deck

• Drawing a set of 7 Scrabble tiles

• Flipping a coin ten times in a row

• Spinning a roulette wheel three times

Mutually Exclusive Events

Events that cannot happen at the same time.

Multiple Choice

Which of the following represents a pair of mutually exclusive events?

• Drawing either a Heart or a King from a deck of cards

• Spinning an odd number or a prime number on a spinner with numbers 1 through 10

• Rolling a 6 on either of a pair of six-sided dice

• Pulling a Scrabble tile from a bag that is a vowel and a consonant.

The Addition Rule

• Measures the probability that one event occurs out of either outcome (OR)

•  $P\left(A\ or\ B\right)$  or  $P\left(A\cup B\right)$  

•  $\cup\longrightarrow$  "union"

Multiple Choice

Suppose you roll a pair of six-sided dice and add them together. What is the probability the result is even OR prime?

• 25/36

• 2/3

• 3/4

• 20/27

Multiple Choice

Suppose you draw a card from the top of a randomly shuffled deck. What is the chance you draw a Heart card or a King card?

( THINK - IS THIS MUTUALLY EXCLUSIVE!?)

• 9/13

• 4/13

• 17/52

• 18/52

Multiplication Rule

• Measures the probability that two events specifically occur in conjunction (AND)

•  $P\left(A\ and\ B\right)$  or  $P\left(A\cap B\right)$  

•  $\cap\rightarrow$  "intersection"

Multiple Choice

On a multiple choice test, you encounter a set of 4 questions, each with 4 possible answer choices, that you have no idea how to answer. You decide to guess randomly on each of these questions and hope for the best. What is the probability that you get all four answers correct?

• 1/4

• 1/2

• 1/64

• 1/256

Exit Ticket

Answer the following questions to check your understanding of today's lesson!

Multiple Choice

Is the event INDEPENDENT or DEPENDENT?

Amy plays card games. She picks a card at random. Then without putting the first card back, he picks a second card at random.

• Independent

• Dependent

Multiple Choice

A glass jar contains 1 red, 3 green, 2 blue, and 4 yellow marbles. If a single marble is chosen at random from the jar, what is the probability that it is yellow or green?

• 3/10

• 4/10

• 7/10

• None of the above

Multiple Choice

The probability of a New York teenager owning a skateboard is 0.37, of owning a bicycle is 0.81 and of owning both is 0.36. If a New York teenager is chosen at random, what is the probability that the teenager owns a skateboard or a bicycle?

• 1.18

• 0.7

• 0.82

• None of the above

Multiple Choice

What is the probability of rolling a die and landing on a 4, and then rolling the die again and landing on any even number?

• 1 ⁄ 6

• 1 ⁄ 8

• 1 ⁄ 2

• 1 ⁄ 12

Multiple Choice

What is the probability of rolling an even number on the first roll of a number cube and rolling an odd number on the second roll?

• 1/4

• 1

• 1/8

• 1/2

Mission Accomplished!

If you didn't find you understand this too well, maybe consider reviewing the lesson later with my recording and making another attempt!