Warm Up: Independent Probability

You spin the spinner two times. The first time it lands on 3, and the second time it lands on 5. These two events are

• Independent Events

• Dependent Events

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

• 1 ⁄ 6

• 1 ⁄ 8

• 1 ⁄ 2

• 1 ⁄ 12

What is the probability of picking a green marble, replace it, then picking green again? (leave answer in fraction form in lowest terms)

• 1/7

• 1

• 1/49

• 0

A coin is flipped and a die is rolled. What is the probability of getting a head on the coin and a 4 on the die?

Two cards are drawn from a deck of 52 cards, one after the other, with replacement. What is the probability that both cards are aces?

Which of the following pairs of events are independent?

• Drawing two cards from a deck without replacement

• Rolling a die and flipping a coin

• Choosing a marble from a bag, not replacing it, and choosing another

• Picking two socks from a drawer without replacement

A bag contains 3 red balls and 2 blue balls. If a ball is drawn and then replaced, what is the probability of drawing a red ball followed by a blue ball?

• 3/10

• 3/5

• 2/5

• 6/25

Which of the following statements is true about independent events?

• The occurrence of one event affects the occurrence of the other.

• The probability of both events occurring is the sum of their individual probabilities.

• The probability of both events occurring is the product of their individual probabilities.

• The events cannot occur at the same time.

A spinner has 4 equal sections colored red, blue, green, and yellow. If the spinner is spun twice, what is the probability of landing on red both times?