Lesson 4 & 5 Quiz - Possibility Diagrams & Tree Diagrams
Lesson 4 & 5 Quiz - Possibility Diagrams & Tree Diagrams. Please go through the lesson before attempting the quiz. This quiz has 15 questions. There will not be any time limit for this quiz and answer all questions. You need to answer at least 10 questions correctly in order to pass the quiz. Please acknowledge by entering you name before attempting the quiz. Good luck!
Questions and Answers
- 1.
X = {3, 4, 5, 6} and Y = {7, 8, 9, 10}. An element x is selected randomly from X and an element y is selected from Y. The value of x + y is then recorded.What is the probability that x + y is odd?
- A.
1 / 8
- B.
1 / 6
- C.
1 / 4
- D.
1 / 2
Correct Answer
D. 1 / 2Explanation
Let E be the event that x + y is odd.
Using the possibility diagram, we can easily see that n(S) = 16 and n(E) = 8.
Therefore, P(E) = 8 / 16 = 1 / 2Rate this question:
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- 2.
X = {3, 4, 5, 6} and Y = {7, 8, 9, 10}. An element x is selected randomly from X and an element y is selected from Y. The value of x + y is then recorded.What is the probability that x + y is even?
- A.
1 / 8
- B.
1 / 6
- C.
1 / 4
- D.
1 / 2
Correct Answer
D. 1 / 2Explanation
Let F be the event that x + y is even.
Using the possibility diagram, we can easily see that n(S) = 16 and n(F) = 8.
Therefore, P(F) = 8 / 16 = 1 / 2Rate this question:
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- 3.
X = {3, 4, 5, 6} and Y = {7, 8, 9, 10}. An element x is selected randomly from X and an element y is selected from Y. The value of xy is then recorded.What is the probability that xy is a multiple of 3?
- A.
3 / 8
- B.
5 / 8
- C.
3 / 16
- D.
5 / 16
Correct Answer
B. 5 / 8Explanation
Let H be the event that xy is a multiple of 3.
Using the possibility diagram, we can easily see that n(S) = 16 and n(H) = 10.
Therefore, P(H) = 10 / 16 = 5 / 8Rate this question:
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- 4.
X = {3, 4, 5, 6} and Y = {7, 8, 9, 10}. An element x is selected randomly from X and an element y is selected from Y. The value of xy is then recorded.What is the probability that xy is less than or equal to 30?
- A.
3 / 8
- B.
5 / 8
- C.
3 / 16
- D.
5 / 16
Correct Answer
D. 5 / 16Explanation
Let H be the event that xy is less than or equal to 30 .
Using the possibility diagram, we can easily see that n(S) = 16 and n(I) = 5.
Therefore, P(I) = 5 / 16 = 5 / 16Rate this question:
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- 5.
In a game, the player throws a coin and a regular die simultaneously. If the coin shows a head, the player's score is the score on the die. If the coin shows a tail, then the player's score is twice the score on the die. What is the probability that the score is even?
- A.
1 / 4
- B.
1 / 2
- C.
3 / 4
- D.
1
Correct Answer
C. 3 / 4Explanation
Let E be the score is even.
Using the possibility diagram, we can easily see that n(S) = 12 and n(E) = 9.
Therefore, P(E) = 9 / 12 = 3 / 4Rate this question:
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- 6.
In a game, the player throws a coin and a regular die simultaneously. If the coin shows a head, the player's score is the score on the die. If the coin shows a tail, then the player's score is twice the score on the die. What is the probability that the score is less than 6?
- A.
5 / 6
- B.
5 / 12
- C.
7 / 12
- D.
3 / 4
Correct Answer
B. 5 / 12Explanation
Let F be the score is even.
Using the possibility diagram, we can easily see that n(S) = 12 and n(F) = 5.
Therefore, P(F) = 5 / 12Rate this question:
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- 7.
A coin is flipped 4 times. What is the value of n(S)?
- A.
4
- B.
8
- C.
12
- D.
16
Correct Answer
D. 16Explanation
Using a tree diagram, we can see that n(S) = 16.Rate this question:
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- 8.
A coin is flipped 4 times. What is the probability of getting more than 2 heads?
- A.
3 / 8
- B.
5 / 8
- C.
3 / 16
- D.
5 / 16
Correct Answer
D. 5 / 16Explanation
Let F be the event of getting more than 2 heads.
Using a tree diagram, we can see that n(F) = 5.
Therefore, P(F) = 5 / 16Rate this question:
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- 9.
A coin is flipped 4 times. What is the probability of getting all 4 coins land on the same side?
- A.
1 / 16
- B.
1 / 8
- C.
1 / 4
- D.
1 / 2
Correct Answer
B. 1 / 8Explanation
Let G be the event of all 4 coins land on the same side.
Using a tree diagram, we can see that n(G) = 2.
Note: 2 possible outcomes - All heads and all tails.
Therefore, P(G) = 2 / 16 = 1 / 8Rate this question:
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- 10.
In a game, a player will have to throw a tetrahedral die and a coin at the same time. If he get a tail on the coin, the game will stop and he will receive the point based on the side facing down on the tetrahedral die. If he get a head on the coin, he will then throw the die again and he will receive the point based on the product of the 2 throws on the die. What are the number of different possible score a player can get?
- A.
4
- B.
8
- C.
9
- D.
16
Correct Answer
C. 9Explanation
From the tree diagram, we can see that the possible scores that the player can score = {1, 2, 3, 4, 6, 8, 9, 12, 16}
Therefore, number of possible scores = 9.Rate this question:
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- 11.
In a game, a player will have to throw a tetrahedral die and a coin at the same time. If he get a tail on the coin, the game will stop and he will receive the point based on the side facing down on the tetrahedral die. If he get a head on the coin, he will then throw the die again and he will receive the point based on the product of the 2 throws on the die. What is the value of n(S)?
- A.
8
- B.
9
- C.
16
- D.
20
Correct Answer
D. 20Explanation
From the tree diagram, we can see that n(S) = 20.Rate this question:
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- 12.
In a game, a player will have to throw a tetrahedral die and a coin at the same time. If he get a tail on the coin, the game will stop and he will receive the point based on the side facing down on the tetrahedral die. If he get a head on the coin, he will then throw the die again and he will receive the point based on the product of the 2 throws on the die. What is the probability of getting a score greater than 7?
- A.
3 / 8
- B.
3 / 10
- C.
3 / 16
- D.
3 / 20
Correct Answer
B. 3 / 10Explanation
Let E be the event of getting a score greater than 7.
From the tree diagram, we can see that n(S) = 20 and n(E) = 6.
Therefore, P(E) = 6 / 20 = 3 / 10Rate this question:
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- 13.
In a game, a player will have to throw a tetrahedral die and a coin at the same time. If he get a tail on the coin, the game will stop and he will receive the point based on the side facing down on the tetrahedral die. If he get a head on the coin, he will then throw the die again and he will receive the point based on the product of the 2 throws on the die. If the player can only wins if he/she get above a certain value. What is the value if the game only allows 2 / 5 of the players to win?
- A.
4
- B.
5
- C.
6
- D.
7
Correct Answer
B. 5Explanation
Let F be the event that the player score more than 5 points.
From the tree diagram, we can see that n(S) = 20 and n(F)= 8.
Therefore, P(F) = 8 / 20 = 4 / 5Rate this question:
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