Probability of Independent Events

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

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

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