Proving Independent Events

Two marbles are drawn from a container in such a way that the first marble drawn is replaced before selecting the second marble. Does the outcome of the first draw affect the outcome of the second?

• Yes

• No

What is the probability of the arrow stopping on “X” on the first spin and “F” on the second spin?

• 5/6

• 1/36

• 1/3

• 1/6

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

Marietta picks a candle from the bunch, replaces it, and then selects one again. What are the chances that she selects a green both times?

• 1/144

• 1/12

• 1/36

• 2/24

• 2/12

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 five or greater if the first card is replaced?

• 1/4

• 2/3

• 3/10

• 3/5

What is the probability that Tom will get a lollipop, replace it, then draw a gumball? The treat bag containing 6 lollipops and 4 gum balls

• 1/24

• 1/90

• 6/25

• 1/10

There are six nickels and seven dimes in your pocket. You randomly pick a coin out of your pocket and then return it to your pocket. Then you randomly pick another coin. What is the probability that both times the coin is a nickel?

• 6/13

• 2/7

• 5/16

• 3/19

• 36/169

A marble bag contains 3 red marbles, 4 gray marbles, 6 white marbles, and 5 black marbles. What is the probability of randomly drawing a red marble and then a gray marble if the first marble is replaced?

• 1/9

• 1/27

• 1/6

• 2/9

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