GATE Exam > GATE Questions > A fair die is rolled two times independently....
Start Learning for Free
A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes is
- a)4
- b)4.5
- c)3
- d)5.5
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A fair die is rolled two times independently. Given that the outcome o...
Let X is a random variable represents an event of rolling a die and P(X = xi) represents the probability of getting sum as xi.
While rolling a die, the probability of getting different numbers as follows.
Most Upvoted Answer
A fair die is rolled two times independently. Given that the outcome o...
Solution:
Given that the first roll is 1. Let E be the event that the sum of the two outcomes is x. We need to find E(x), the expected value of the sum of two outcomes.
Let A be the event that the first roll is 1.
The probability of getting 1 on the first roll is 1/6.
The probability of getting x-1 on the second roll is 1/6.
Therefore, P(A∩E) = P(A) * P(E|A) = 1/6 * 1/6 = 1/36.
Now, we need to find the sum of all possible outcomes.
The possible outcomes are (1,1), (1,2), (1,3), (1,4), (1,5), and (1,6).
Their corresponding sums are 2, 3, 4, 5, 6, and 7.
E(x) = ∑x * P(E(x))
= (2 * 1/36) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) + (7 * 1/6)
= 4.5
Therefore, the expected value of the sum of two outcomes is 4.5.
Hence, the correct answer is option 'B'.
Given that the first roll is 1. Let E be the event that the sum of the two outcomes is x. We need to find E(x), the expected value of the sum of two outcomes.
Let A be the event that the first roll is 1.
The probability of getting 1 on the first roll is 1/6.
The probability of getting x-1 on the second roll is 1/6.
Therefore, P(A∩E) = P(A) * P(E|A) = 1/6 * 1/6 = 1/36.
Now, we need to find the sum of all possible outcomes.
The possible outcomes are (1,1), (1,2), (1,3), (1,4), (1,5), and (1,6).
Their corresponding sums are 2, 3, 4, 5, 6, and 7.
E(x) = ∑x * P(E(x))
= (2 * 1/36) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) + (7 * 1/6)
= 4.5
Therefore, the expected value of the sum of two outcomes is 4.5.
Hence, the correct answer is option 'B'.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer?
Question Description
A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer?.
A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer?.
Solutions for A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.
Here you can find the meaning of A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A fair die is rolled two times independently. Given that the outcome on the first roll is 1, the expected value of the sum of the two outcomes isa)4b)4.5c)3d)5.5Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GATE tests.
|
|
Explore Courses for GATE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup