GATE Exam > GATE Questions > A die is rolled three times. The probability ...
Start Learning for Free
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes is
- a)1/6
- b)3/8
- c)1/8
- d)1/2
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
A die is rolled three times. The probability that exactly one odd numb...
Probability of getting an odd number in rolling of a die = 3/6 = 1/2.
Now using binomial distribution
P(Exactly one odd number among three outcomes)
Now using binomial distribution
P(Exactly one odd number among three outcomes)
Most Upvoted Answer
A die is rolled three times. The probability that exactly one odd numb...
**Solution:**
To solve this problem, we need to find the probability of getting exactly one odd number when a die is rolled three times.
**Step 1: Finding the Sample Space**
When a die is rolled once, the possible outcomes are numbers from 1 to 6. So, when a die is rolled three times, the sample space consists of all possible combinations of three numbers from 1 to 6.
The total number of outcomes in the sample space is given by 6^3 = 216, since each roll has 6 possible outcomes and there are 3 rolls.
**Step 2: Finding the Favorable Outcomes**
To find the favorable outcomes, we need to consider the cases where only one odd number appears in the three rolls.
Case 1: Odd number in the first roll
In this case, we have three options for the odd number (1, 3, or 5), and for each odd number, there are three options for the even numbers (2, 4, or 6) in the remaining two rolls. So, the number of favorable outcomes for this case is 3 * 3 = 9.
Case 2: Odd number in the second roll
Similarly, we have three options for the odd number in the second roll and three options for the even numbers in the first and third rolls. So, the number of favorable outcomes for this case is also 3 * 3 = 9.
Case 3: Odd number in the third roll
Again, we have three options for the odd number in the third roll and three options for the even numbers in the first and second rolls. So, the number of favorable outcomes for this case is 3 * 3 = 9.
**Step 3: Calculating the Probability**
The total number of favorable outcomes is given by 9 + 9 + 9 = 27.
Therefore, the probability of getting exactly one odd number is 27/216 = 3/24 = 3/8.
Hence, the correct answer is option b) 3/8.
To solve this problem, we need to find the probability of getting exactly one odd number when a die is rolled three times.
**Step 1: Finding the Sample Space**
When a die is rolled once, the possible outcomes are numbers from 1 to 6. So, when a die is rolled three times, the sample space consists of all possible combinations of three numbers from 1 to 6.
The total number of outcomes in the sample space is given by 6^3 = 216, since each roll has 6 possible outcomes and there are 3 rolls.
**Step 2: Finding the Favorable Outcomes**
To find the favorable outcomes, we need to consider the cases where only one odd number appears in the three rolls.
Case 1: Odd number in the first roll
In this case, we have three options for the odd number (1, 3, or 5), and for each odd number, there are three options for the even numbers (2, 4, or 6) in the remaining two rolls. So, the number of favorable outcomes for this case is 3 * 3 = 9.
Case 2: Odd number in the second roll
Similarly, we have three options for the odd number in the second roll and three options for the even numbers in the first and third rolls. So, the number of favorable outcomes for this case is also 3 * 3 = 9.
Case 3: Odd number in the third roll
Again, we have three options for the odd number in the third roll and three options for the even numbers in the first and second rolls. So, the number of favorable outcomes for this case is 3 * 3 = 9.
**Step 3: Calculating the Probability**
The total number of favorable outcomes is given by 9 + 9 + 9 = 27.
Therefore, the probability of getting exactly one odd number is 27/216 = 3/24 = 3/8.
Hence, the correct answer is option b) 3/8.
|
Explore Courses for GATE exam
|
|
Similar GATE Doubts
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct answer is option 'B'. Can you explain this answer?
Question Description
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct 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 die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct 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 die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct answer is option 'B'. Can you explain this answer?.
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct 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 die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct 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 die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct answer is option 'B'. Can you explain this answer?.
Solutions for A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct 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 die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A die is rolled three times. The probability that exactly one odd number turns up among the three outcomes isa)1/6b)3/8c)1/8d)1/2Correct 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