Which of the following pairs of events is dependent?

Taking a colored ball from a basket. Without replacement, drawing another ball.

Rolling a die. Rolling the die again.

Drawing a card from a deck of 52. Replacing the card and drawing again.

Probability Of Simple And Compound Events

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| By MIRIAM

MIRIAM

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Quizzes Created: 2 | Total Attempts: 1,742

Questions: 15 | Attempts: 367 | Updated: Mar 21, 2023

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Probability Of Simple And Compound Events - Quiz

Use this practice quiz to help you review the lessons on Probability of Simple and Compound Events.

Questions and Answers

1.

A card is randomly selected from a standard 52-card deck. Find the probability that the card selected is either a queen or a 3?

Explanation
The probability of selecting a queen from a standard 52-card deck is 4/52, as there are 4 queens in the deck. The probability of selecting a 3 is also 4/52, as there are 4 threes in the deck. Since we are interested in the probability of selecting either a queen or a 3, we can add these two probabilities together to get 8/52 or 2/13.

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0
4 1
2.

Probabilities can only be between 0 and 1 (both 0 and 1 included).
- A.
  
  True
- B.
  
  False
Correct Answer
A. True

Explanation
The statement is true because probabilities represent the likelihood of an event occurring, and they can only range from 0 to 1. A probability of 0 means that the event will not occur, while a probability of 1 means that the event is certain to occur. Any value outside of this range would not make sense in the context of probabilities. Therefore, the statement is correct.

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3.

Which of the following pairs of events is dependent?
- A.
  
  Rolling a die. Rolling the die again.
- B.
  
  Drawing a card from a deck of 52. Replacing the card and drawing again.
- C.
  
  Taking a colored ball from a basket. Without replacement, drawing another ball.
- D.
  
  Flipping a coin three times.
Correct Answer
C. Taking a colored ball from a basket. Without replacement, drawing another ball.

Explanation
Taking a colored ball from a basket and drawing another ball without replacement are dependent events. This is because the outcome of the second event is influenced by the outcome of the first event. When a ball is taken from the basket, the total number of balls in the basket decreases, which affects the probability of drawing a specific ball on the second draw.

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4.

You flip a coin twice. What is P(heads, heads)?
- A.
  
  1/2
- B.
  
  1/4
- C.
  
  3/7
- D.
  
  2/1
Correct Answer
B. 1/4

Explanation
When flipping a fair coin twice, there are four possible outcomes: heads-heads, heads-tails, tails-heads, and tails-tails. Since each flip is independent, the probability of getting heads on the first flip is 1/2, and the probability of getting heads on the second flip is also 1/2. Therefore, the probability of getting heads on both flips (heads-heads) is (1/2) * (1/2) = 1/4.

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5.

You pick a marble at random. When you put the first marble back, you select a second marble at random. What is P(green, orange)?
- A.
  
  1/11
- B.
  
  2/3
- C.
  
  1/12
- D.
  
  5/48
Correct Answer
D. 5/48

Explanation
When you pick a marble at random, there are a total of 12 marbles in the bag. Out of these 12 marbles, 5 are green and 3 are orange. After putting the first marble back, the total number of marbles remains the same. Therefore, when you select the second marble at random, the probability of getting a green marble is still 5/12. Since both events are independent, the probability of getting both a green and an orange marble is the product of their individual probabilities, which is (5/12) * (3/12) = 5/48.

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6.

You toss a coin and obtained a head, and you rolled a 6-sided die and obtained a 5. What type of events are they?
- A.
  
  Independent Events
- B.
  
  Dependent Events
Correct Answer
A. Independent Events

Explanation
The coin toss and rolling the die are independent events because the outcome of one event does not affect the outcome of the other event. The result of obtaining a head on the coin toss has no impact on the result of obtaining a 5 on the die roll.

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7.

A bag contains 3 red cubes, 4 green cubes, and 5 blue cubes. One cube is taken from the bag and is not replaced. Another cube is taken.
- A.
  
  Dependent
- B.
  
  Independent
Correct Answer
A. Dependent

Explanation
The answer is "Dependent" because the probability of choosing the second cube depends on the outcome of the first cube. Since the first cube is not replaced, the composition of the bag changes after each draw. Therefore, the probability of selecting a certain color cube for the second draw is affected by the removal of the first cube.

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8.

Spinning a number 6 and then spinning a number 5 on the same spinner.
- A.
  
  Independent Events
- B.
  
  Dependent Events
Correct Answer
A. Independent Events

Explanation
The given scenario involves spinning a number 6 and then spinning a number 5 on the same spinner. These events are considered independent because the outcome of spinning a number 6 does not affect the outcome of spinning a number 5. The probability of spinning a number 6 and the probability of spinning a number 5 are not dependent on each other.

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9.

A spinner numbered 1 through 10 is spun 100 times. The results of the experiment are shown in the table below. What is the experimental probability of spinning an 8?
- A.
  
  7/100
- B.
  
  1/100
- C.
  
  13/100
- D.
  
  10/100
Correct Answer
C. 13/100

Explanation
The experimental probability of spinning an 8 is 13/100 because out of the 100 spins, the number 8 appeared 13 times.

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10.

A set of 15 cards is numbered 1, 2, 3, …, 15. Suppose you choose one card at random without looking. What is the probability of choosing an odd-numbered card?
- A.
  
  1/2
- B.
  
  7/15
- C.
  
  1/15
- D.
  
  8/15
Correct Answer
D. 8/15

Explanation
There are a total of 15 cards, out of which 8 are odd-numbered (1, 3, 5, 7, 9, 11, 13, 15). Therefore, the probability of choosing an odd-numbered card is 8/15.

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11.

From left to right on the number line, order the events based on how likely they are to occur. a. The event is certain to happen. b. The event is just as likely to happen as not to happen. c. The event has no chance of happening. d. The event could happen but is unlikely. e. The event is likely to happen.
- A.
  
  A, e, b, d, c
- B.
  
  D, c, b, e, a
- C.
  
  D, c, b, a, e
- D.
  
  C, d, b, e, a
Correct Answer
D. C, d, b, e, a

Explanation
The events are ordered from least likely to most likely to occur. The event that has no chance of happening (c) is the least likely, followed by the event that could happen but is unlikely (d). The event that is just as likely to happen as not to happen (b) is next, followed by the event that is likely to happen (e). Finally, the event that is certain to happen (a) is the most likely to occur.

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12.

Something that is unlikely to happen has a probability of between
- A.
  
  1 and 2
- B.
  
  0.5 and 1
- C.
  
  0 and 0.5
Correct Answer
C. 0 and 0.5

Explanation
The correct answer is 0 and 0.5 because a probability value between 0 and 0.5 indicates that the event is unlikely to happen. A probability of 0 means that the event will not occur at all, while a probability of 0.5 means that there is a 50% chance of the event happening. Therefore, something that is unlikely to happen falls within this range of probabilities.

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13.

A bag contains just 5 buttons, all of which are blue. What is the probability of picking a red button from the bag?
- A.
  
  0.5
- B.
  
  1
- C.
  
  0
Correct Answer
C. 0

Explanation
Since the bag contains only blue buttons, there are no red buttons to pick from. Therefore, the probability of picking a red button from the bag is 0.

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14.

M A T H E M A T I C S ( Each letter represents a card) You select a card at random. Without replacing the card, you select a second card. Find the probability. P(M, then H)

Correct Answer
1/55, 0.0181

Explanation
When selecting a card at random without replacement, the probability of selecting the letter "M" first is 1 out of the total number of cards, which is 55. After selecting the "M" card, there are now 54 cards left, and the probability of selecting the letter "H" second is 1 out of 54. Therefore, the probability of selecting "M" first and then "H" second is 1/55 multiplied by 1/54, which simplifies to 0.0181.

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4
15.

You have 15 coins in your pocket. 3 of the coins are Chinese yuan. Suppose you pick a coin out of your pocket at random. Find P(not Chinese yuan).
- A.
  
  3/15
- B.
  
  11/15
- C.
  
  1
- D.
  
  None of the above
Correct Answer
D. None of the above

Explanation
The correct answer is 12/15. Since there are 15 coins in total and 3 of them are Chinese yuan, there are 12 coins that are not Chinese yuan. Therefore, the probability of picking a coin that is not Chinese yuan is 12/15.

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Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
May 19, 2020

Quiz Created by
MIRIAM

Probability Of Simple And Compound Events

A card is randomly selected from a standard 52-card deck. Find the probability that the card selected is either a queen or a 3?

Probabilities can only be between 0 and 1 (both 0 and 1 included).

Which of the following pairs of events is dependent?

You flip a coin twice. What is P(heads, heads)?

You pick a marble at random. When you put the first marble back, you select a second marble at random. What is P(green, orange)?

You toss a coin and obtained a head, and you rolled a 6-sided die and obtained a 5. What type of events are they?

A bag contains 3 red cubes, 4 green cubes, and 5 blue cubes. One cube is taken from the bag and is not replaced. Another cube is taken.

Spinning a number 6 and then spinning a number 5 on the same spinner.

A spinner numbered 1 through 10 is spun 100 times. The results of the experiment are shown in the table below. What is the experimental probability of spinning an 8?

A set of 15 cards is numbered 1, 2, 3, …, 15. Suppose you choose one card at random without looking. What is the probability of choosing an odd-numbered card?

Something that is unlikely to happen has a probability of between

A bag contains just 5 buttons, all of which are blue. What is the probability of picking a red button from the bag?

M A T H E M A T I C S ( Each letter represents a card) You select a card at random. Without replacing the card, you select a second card. Find the probability. P(M, then H)

You have 15 coins in your pocket. 3 of the coins are Chinese yuan. Suppose you pick a coin out of your pocket at random. Find P(not Chinese yuan).