Dependent and Independent Events in Probability

A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn. Are the two events dependent or independent?

• Independent

• Dependent

Suppose a number cube is rolled twice. What is the probability that an odd number will show both times?

• 1/3

• 1/2

• 1/6

• 1/4

A number cube is rolled and a coin is tossed. What is the probability of rolling a number greater than 4 and tossing tails?

• 1/6

• 1/3

• 1/2

• 1/4

Ten cards numbered 1-10 are placed in a hat. What is the probability of randomly drawing a card with an even number then a card with a number greater than or equal to five if the first card is replaced?

• 1/4

• 2/3

• 3/10

• 3/5

Independent events: the occurrence of one event ​ (a)   the probability of another event

Dependent events: the occurrence of one event ​ (b)   the probability of another event (sometimes called “not independent”)

• does not affect

• does affect

Flipping two coins is an example of ​ (a)   events because the result of one event ​ (b)   affect the result of the other. Drawing two cards from a deck is an example of ​ (c)   events because the result of one event ​ (d)   affect the result of the other.

• Independent

• does not

• Dependent

• does

A bag contains some red-colored and some blue-colored marbles. First a red-colored marble is drawn and then, without replacing the first marble, a blue-colored marble is drawn. Are the two events dependent or independent? (a)  

• Independent

• Dependent

Determine whether each scenario below represents an independent event or dependent event. Flipping a coin and spinning a spinner.

• Independent

• Drawing a Queen from a deck of cards, then drawing a 10

• Dependent

• Drawing an Ace from a deck of cards, replacing it, then drawing a King

• Independent

• Rolling a fair six-sided die and getting an A on your next test

• Dependent

• Selecting a marble from a bad, not replacing it, and selecting another marble from the bag

• Independent

• Flipping a coin and spinning a spinner

Determine if each event represents dependent or independent probability.

Flipping three coins​ (a)  

Drawing candy from a bag, not replacing it , then selecting another piece​ (b)  

Getting a marble of a bag, replacing it, then getting another​ (c)  

• independent

• dependent

Match the following based on whether it would independent or dependent probability.

• Independent

• Selecting 2 students for Knights at the Round Table

• Dependent

• Taking a marble out of a bag, replacing it, then picking another

• Independent

• Taking a piece of candy from a bag, eating it, then picking another

• Dependent

• Flipping 2 coins

• Independent

• Spinning a spinner and rolling a die