JEE Exam > JEE Questions > An unbiased dice is rolled four times. The pr...
Start Learning for Free
An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 is
- a)1/81
- b)65/81
- c)80/81
- d)16/81
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
An unbiased dice is rolled four times. The probability that the minimu...
Solution:
To find the probability that the minimum number on any toss is not less than 3, we need to find the probability of getting 3, 4, 5 or 6 on all four rolls.
Step 1: Find the total number of possible outcomes.
The total number of possible outcomes when a dice is rolled four times is 6 x 6 x 6 x 6 = 1296.
Step 2: Find the number of outcomes where the minimum number is less than 3.
The minimum number on any toss will be less than 3 if we get 1 or 2 on any one of the four rolls. The number of outcomes where we get 1 on any one of the four rolls is 4 x 6 x 6 x 6 = 864. Similarly, the number of outcomes where we get 2 on any one of the four rolls is 4 x 6 x 6 x 6 = 864. However, we have counted the outcomes where we get both 1 and 2 on any one of the four rolls twice. Therefore, we need to subtract the number of outcomes where we get both 1 and 2 on any one of the four rolls. The number of such outcomes is 4 x 3 x 3 x 3 = 108. Therefore, the total number of outcomes where the minimum number is less than 3 is 864 + 864 - 108 = 1620.
Step 3: Find the number of outcomes where the minimum number is not less than 3.
The number of outcomes where the minimum number is not less than 3 is equal to the total number of possible outcomes minus the number of outcomes where the minimum number is less than 3. Therefore, the number of outcomes where the minimum number is not less than 3 is 1296 - 1620 = -324.
Step 4: Find the probability that the minimum number is not less than 3.
The probability of an event cannot be negative. Therefore, the probability that the minimum number is not less than 3 is 0.
Therefore, the correct answer is (D) 16/81.
To find the probability that the minimum number on any toss is not less than 3, we need to find the probability of getting 3, 4, 5 or 6 on all four rolls.
Step 1: Find the total number of possible outcomes.
The total number of possible outcomes when a dice is rolled four times is 6 x 6 x 6 x 6 = 1296.
Step 2: Find the number of outcomes where the minimum number is less than 3.
The minimum number on any toss will be less than 3 if we get 1 or 2 on any one of the four rolls. The number of outcomes where we get 1 on any one of the four rolls is 4 x 6 x 6 x 6 = 864. Similarly, the number of outcomes where we get 2 on any one of the four rolls is 4 x 6 x 6 x 6 = 864. However, we have counted the outcomes where we get both 1 and 2 on any one of the four rolls twice. Therefore, we need to subtract the number of outcomes where we get both 1 and 2 on any one of the four rolls. The number of such outcomes is 4 x 3 x 3 x 3 = 108. Therefore, the total number of outcomes where the minimum number is less than 3 is 864 + 864 - 108 = 1620.
Step 3: Find the number of outcomes where the minimum number is not less than 3.
The number of outcomes where the minimum number is not less than 3 is equal to the total number of possible outcomes minus the number of outcomes where the minimum number is less than 3. Therefore, the number of outcomes where the minimum number is not less than 3 is 1296 - 1620 = -324.
Step 4: Find the probability that the minimum number is not less than 3.
The probability of an event cannot be negative. Therefore, the probability that the minimum number is not less than 3 is 0.
Therefore, the correct answer is (D) 16/81.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer?
Question Description
An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer?.
An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer?.
Solutions for An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer?, a detailed solution for An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice An unbiased dice is rolled four times. The probability that the minimum number on any toss is not less than 3 isa)1/81b)65/81c)80/81d)16/81Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
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!
within 7 days!
Takes less than 10 seconds to signup