Two dice are thrown and the side of both dice facing up are observed. Which of the following events are mutually exclusive events?

E: One of the dice shows a 2. F: The sum is greater than 8.

A: Both dice are the same number. B: Both dice are even number.

C: The sum of both dice is even. D: The sum of both dice is a prime number.

G: The product of both dice is even. H: The sum of both dice is odd.

Lesson 6 Quiz - Addition Of Probabilities And Mutually Exclusive Events

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Lesson 6 Quiz - Addition Of Probabilities And Mutually Exclusive Events - Quiz

Lesson 4 & 5 Quiz - Addition of Probabilities and Mutually Exclusive Events. Please go through the lesson before attempting the quiz. This quiz has 10 questions. There will not be any time limit for this quiz and answer all questions. You need to answer at least 7 questions correctly in order to pass the quiz. Please acknowledge by entering you name before attempting the quiz. Good luck!

Questions and Answers

1.

Two dice are thrown and the side of both dice facing up are observed. Which of the following events are mutually exclusive events?
- A.
  
  A: Both dice are the same number. B: Both dice are even number.
- B.
  
  C: The sum of both dice is even. D: The sum of both dice is a prime number.
- C.
  
  E: One of the dice shows a 2. F: The sum is greater than 8.
- D.
  
  G: The product of both dice is even. H: The sum of both dice is odd.
Correct Answer
C. E: One of the dice shows a 2. F: The sum is greater than 8.

Explanation
E= {(1,2), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,2), (4,2), (5,2), (6,2)}

F= {(3,6), (4,5), (4,6), (5,4), (5,5), (5,6), (6,5), (6,6)}

Therefore, events E and F are mutually exclusive events.

B= {(

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2.

In a basketball tournament, 3 of the participating teams - Lion, Panther and Jaguar have the probabilities of 4/15, 3/10 and 1/5 respectively of winning the tournament. Find the probability that Lion or Jaguar will win the tournament.
- A.
  
  1 / 15
- B.
  
  1 / 2
- C.
  
  7 / 15
- D.
  
  17 / 30
Correct Answer
C. 7 / 15

Explanation
Let L be the event Lion will win the tournament and J be the event Jaguar will win the tournament.

L and J are mutually exclusive events.

Therefore, P(L or J) = P(L) + P(J) = 4/15 + 1/5 = 14/30 = 7/15

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3.

In a basketball tournament, 3 of the participating teams - Lion, Panther and Jaguar have the probabilities of 4/15, 3/10 and 1/5 respectively of winning the tournament. Find the probability that neither Panther nor Jaguar will win the tournament.
- A.
  
  14 / 25
- B.
  
  13 / 30
- C.
  
  8 / 15
- D.
  
  1 / 2
Correct Answer
D. 1 / 2

Explanation
Let P be the event Panther will win the tournament and J be the event Jaguar will win the tournament.

P and J are mutually exclusive events.

P(neither P nor J) = 1 - P(P or J) = 1 - (9/30 + 6/30) = 1 - 15/30 = 1 - 1/2 = 1/2

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4.

In a basketball tournament, 3 of the participating teams - Lion, Panther and Jaguar have the probabilities of 4/15, 3/10 and 1/5 respectively of winning the tournament. Find the probability that neither of the 3 teams will win the tournament.
- A.
  
  7 / 30
- B.
  
  23 / 30
- C.
  
  2 / 75
- D.
  
  73 / 75
Correct Answer
A. 7 / 30

Explanation
Let L be the event Lion will win the tournament, P be the event Panther will win the tournament and J be the event Jaguar will win the tournament.

L, P and J are mutually exclusive events.

P(neither L, P nor J) = 1 - P(L,P or J) = 1 - (4/15 + 9/30 + 6/30) = 1 - 23/30 = 7/30

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5.

The letters of the word 'MUTUALLY' and the word 'EXCLUSIVE' are written on individual cards and the cards are put into a box. A card is picked at random. What is the probability of picking the letter 'U' or 'E'?
- A.
  
  1 / 6
- B.
  
  2 / 17
- C.
  
  5 / 12
- D.
  
  5 / 17
Correct Answer
D. 5 / 17

Explanation
Let U be the event for picking the letter U and E be the event for picking the letter E.

U and E are mutually exclusive events.

Therefore, P(U or E) = P(U) + P(E) = 3/17 + 2/17 = 5/17

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6.

The letters of the word 'MUTUALLY' and the word 'EXCLUSIVE' are written on individual cards and the cards are put into a box. A card is picked at random. What is the probability of picking the letter 'U' or a consonant?
- A.
  
  2 / 3
- B.
  
  13 / 17
- C.
  
  9 / 17
- D.
  
  11 / 17
Correct Answer
B. 13 / 17

Explanation
Let U be the event for picking the letter U and C be the event for picking a consonant.

U and C are mutually exclusive events. Note: U is not a consonant.

Therefore, P(U or C) = P(U) + P(C) = 3/17 + 10/17 = 13/17

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7.

The letters of the word 'MUTUALLY' and the word 'EXCLUSIVE' are written on individual cards and the cards are put into a box. A card is picked at random. What is the probability of not picking the letter 'U' or 'E' or 'L'?
- A.
  
  2 / 3
- B.
  
  3 / 4
- C.
  
  8 / 17
- D.
  
  9 / 17
Correct Answer
D. 9 / 17

Explanation
Let U be the event for picking the letter U, E be the even for picking the letter E and L be the event for picking the letter L.

U, E and L are mutually exclusive events.

P(neither U, E or L) = 1 - P(U, E or L) = 1 - (3/17 + 2/17 + 3/17) = 1 - 8/17 = 9/17

U and C are mutually exclusive events. Note: U is not a consonant.

Therefore, P(U or C) = P(U) + P(C) = 3/17 + 10/17 = 13/17

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8.

Ten cards numbered 11, 12, 13, 14, ..., 20 are placed in a box. A card is removed at random from the box. Find the probability that the number on the card is either even or prime.
- A.
  
  1 / 5
- B.
  
  1 / 2
- C.
  
  2 / 5
- D.
  
  9 / 10
Correct Answer
D. 9 / 10

Explanation
Let E be the event that the number of the card is an even number and P be the event that the number of the card is a prime.

P(E or P) = P(E) + P(P) = 5/10 + 4/10 = 9/10

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1
0
9.

Ten cards numbered 11, 12, 13, 14, ..., 20 are placed in a box. A card is removed at random from the box. Find the probability that the number on the card is either even or divisible by 3.
- A.
  
  2 / 5
- B.
  
  3 / 5
- C.
  
  4 / 5
- D.
  
  3 / 20
Correct Answer
B. 3 / 5

Explanation
Let E be the event that the number of the card is even and T be the event that the number is divisible by 3.

E and T are NOT mutually exclusive events.

E or T = {12, 14, 15, 16, 18, 20}

P(E or T) = n(E or T) / n(S) = 6/10 = 3/5

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10.

Ten cards numbered 11, 12, 13, 14, ..., 20 are placed in a box. A card is removed at random from the box. Find the probability that the number on the card is either odd or prime.
- A.
  
  3 / 5
- B.
  
  2 / 5
- C.
  
  9 / 10
- D.
  
  1 / 2
Correct Answer
D. 1 / 2

Explanation
Let O be the event that the number of the card is odd and P be the event that the number is prime.

O and P are not mutually exclusive events.

Note: ALL prime numbers (except 2) are odd number. Therefore, P(O or P) = P(O)

P(O or P) = P(O) = 5/10 = 1/2

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Lesson 6 Quiz - Addition Of Probabilities And Mutually Exclusive Events

Two dice are thrown and the side of both dice facing up are observed. Which of the following events are mutually exclusive events?

In a basketball tournament, 3 of the participating teams - Lion, Panther and Jaguar have the probabilities of 4/15, 3/10 and 1/5 respectively of winning the tournament. Find the probability that Lion or Jaguar will win the tournament.

In a basketball tournament, 3 of the participating teams - Lion, Panther and Jaguar have the probabilities of 4/15, 3/10 and 1/5 respectively of winning the tournament. Find the probability that neither Panther nor Jaguar will win the tournament.

In a basketball tournament, 3 of the participating teams - Lion, Panther and Jaguar have the probabilities of 4/15, 3/10 and 1/5 respectively of winning the tournament. Find the probability that neither of the 3 teams will win the tournament.

The letters of the word 'MUTUALLY' and the word 'EXCLUSIVE' are written on individual cards and the cards are put into a box. A card is picked at random. What is the probability of picking the letter 'U' or 'E'?

The letters of the word 'MUTUALLY' and the word 'EXCLUSIVE' are written on individual cards and the cards are put into a box. A card is picked at random. What is the probability of picking the letter 'U' or a consonant?

The letters of the word 'MUTUALLY' and the word 'EXCLUSIVE' are written on individual cards and the cards are put into a box. A card is picked at random. What is the probability of not picking the letter 'U' or 'E' or 'L'?

Ten cards numbered 11, 12, 13, 14, ..., 20 are placed in a box. A card is removed at random from the box. Find the probability that the number on the card is either even or prime.

Ten cards numbered 11, 12, 13, 14, ..., 20 are placed in a box. A card is removed at random from the box. Find the probability that the number on the card is either even or divisible by 3.

Ten cards numbered 11, 12, 13, 14, ..., 20 are placed in a box. A card is removed at random from the box. Find the probability that the number on the card is either odd or prime.