Independent Events Lesson Check

1) If you flip a coin and roll a 6-sided die, what is the probability that you will flip a tails and roll a 2?

1/18

1/12

1/24

1/3

The probability of flipping a tails is 1/2, as there are two possible outcomes (heads or tails) and they are equally likely. The probability of rolling a 2 on a 6-sided die is 1/6, as there is one favorable outcome (rolling a 2) out of six possible outcomes (rolling a number from 1 to 6). To find the probability of both events happening, we multiply the probabilities together: (1/2) * (1/6) = 1/12. Therefore, the probability of flipping a tails and rolling a 2 is 1/12.

Explanation

The probability of flipping a tails is 1/2, as there are two possible outcomes (heads or tails) and they are equally likely. The probability of rolling a 2 on a 6-sided die is 1/6, as there is one favorable outcome (rolling a 2) out of six possible outcomes (rolling a number from 1 to 6). To find the probability of both events happening, we multiply the probabilities together: (1/2) * (1/6) = 1/12. Therefore, the probability of flipping a tails and rolling a 2 is 1/12.

2) Michael Beasley is shooting free throws. Making or missing free throws doesn't change the probability that he will make his next one, and he makes his free throws 75%, percent of the time. What is the probability of Michael Beasley making all of his next 4 free throw attempts?

.75^8

.375^4

.75^4

1.50^2

The probability of Michael Beasley making each free throw is 75%. Since making or missing free throws doesn't change the probability of making the next one, the probability of him making all 4 of his next free throw attempts is calculated by multiplying the individual probabilities together. Therefore, the correct answer is .75^4.

Explanation

The probability of Michael Beasley making each free throw is 75%. Since making or missing free throws doesn't change the probability of making the next one, the probability of him making all 4 of his next free throw attempts is calculated by multiplying the individual probabilities together. Therefore, the correct answer is .75^4.

3) What is the probability(fraction) that you will roll two 3's in a row, on a fair 6-sided die?

1/6

1/36

1/3

1/1

The probability of rolling a 3 on a fair 6-sided die is 1/6. Since we want to roll two 3's in a row, we need to multiply the probabilities together. Therefore, the probability of rolling two 3's in a row is (1/6) * (1/6) = 1/36.

Explanation

The probability of rolling a 3 on a fair 6-sided die is 1/6. Since we want to roll two 3's in a row, we need to multiply the probabilities together. Therefore, the probability of rolling two 3's in a row is (1/6) * (1/6) = 1/36.

4) If you flip a coin and roll a 6-sided die, what is the probability that you will flip a heads and roll at least a 3?

1/2

4/18

4/12

4/24

The probability of flipping a heads is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely. The probability of rolling at least a 3 on a 6-sided die is 4/6 since there are four favorable outcomes (rolling a 3, 4, 5, or 6) out of six possible outcomes. To find the probability of both events happening, we multiply the probabilities together, giving us (1/2) * (4/6) = 4/12. Therefore, the correct answer is 4/12.

Explanation

The probability of flipping a heads is 1/2 since there are two possible outcomes (heads or tails) and they are equally likely. The probability of rolling at least a 3 on a 6-sided die is 4/6 since there are four favorable outcomes (rolling a 3, 4, 5, or 6) out of six possible outcomes. To find the probability of both events happening, we multiply the probabilities together, giving us (1/2) * (4/6) = 4/12. Therefore, the correct answer is 4/12.

5) Captain Kevin has a ship, the H.M.S. Khan. The ship is two furlongs from the Dread Pirate and his merciless band of thieves. The Captain has a 3/5 chance of hitting the Dread Pirate's ship with a cannon. The Dread Pirate only has one good eye, so he will hit the Captain's ship with probability 1/5 of hitting the captains ship with a cannon. If both fire their cannons at the same time, what is the probability that the Captain hits the Dread Pirate's ship, but the Dread Pirate misses?

3/25

12/20

3/15

12/25

The probability that the Captain hits the Dread Pirate's ship is 3/5, and the probability that the Dread Pirate misses the Captain's ship is 4/5 (since he has a 1/5 chance of hitting). To find the probability that both events occur, we multiply the probabilities together: (3/5) * (4/5) = 12/25. Therefore, the probability that the Captain hits the Dread Pirate's ship, but the Dread Pirate misses, is 12/25.

Explanation

The probability that the Captain hits the Dread Pirate's ship is 3/5, and the probability that the Dread Pirate misses the Captain's ship is 4/5 (since he has a 1/5 chance of hitting). To find the probability that both events occur, we multiply the probabilities together: (3/5) * (4/5) = 12/25. Therefore, the probability that the Captain hits the Dread Pirate's ship, but the Dread Pirate misses, is 12/25.

Independent Events Lesson Check

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