Independent Events Lesson Check

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| By Gavinj

Gavinj

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Quizzes Created: 1 | Total Attempts: 633

Questions: 5 | Attempts: 633 | Updated: Mar 21, 2023

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This 'Independent Events Lesson Check' assesses understanding of probability through practical scenarios. It includes calculating chances of dice rolls, coin flips, and free throw shots, focusing on independent event probabilities.

Questions and Answers

1.

What is the probability(fraction) that you will roll two 3's in a row, on a fair 6-sided die?
- A.
  
  1/6
- B.
  
  1/36
- C.
  
  1/3
- D.
  
  1/1
Correct Answer
B. 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.

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2.

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?
- A.
  
  1/18
- B.
  
  1/12
- C.
  
  1/24
- D.
  
  1/3
Correct Answer
B. 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.

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3.

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?
- A.
  
  3/25
- B.
  
  12/20
- C.
  
  3/15
- D.
  
  12/25
Correct Answer
D. 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.

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4.

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?
- A.
  
  .75^8
- B.
  
  .375^4
- C.
  
  .75^4
- D.
  
  1.50^2
Correct Answer
C. .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.

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5.

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?
- A.
  
  1/2
- B.
  
  4/18
- C.
  
  4/12
- D.
  
  4/24
Correct Answer
C. 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.

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Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
Apr 16, 2018

Quiz Created by
Gavinj

Independent Events Lesson Check

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

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?

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?

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?