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An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is
- a)16/81
- b)1/81
- c)80/81
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times...
Solution:
To find the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, we need to find the probability of getting the following results in four rolls:
- The minimum face value is 2, 3, 4, or 5
- The maximum face value is 2, 3, 4, or 5
Let's consider each of these separately.
Probability of minimum face value being 2, 3, 4, or 5:
- The probability of getting any one of these face values on a single roll is 4/6 = 2/3.
- Since we are rolling the die four times, the probability of getting any one of these face values on all four rolls is (2/3)^4 = 16/81.
- However, we need to consider all the possible ways in which these face values can occur in the four rolls. There are 4 possible positions for the minimum face value (first, second, third, or fourth roll), and for each position, there are 4 possible face values (2, 3, 4, or 5). Therefore, there are a total of 4x4 = 16 possible combinations of four rolls that satisfy the condition that the minimum face value is not less than 2.
- For each of these 16 combinations, the maximum face value can be any one of the 4 values 2, 3, 4, or 5, with equal probability. Therefore, the probability of getting a maximum face value that is not greater than 5, given that the minimum face value is not less than 2, is also 1/4.
- Therefore, the overall probability of getting a minimum face value that is not less than 2 and a maximum face value that is not greater than 5 is:
(16/81) x (1/4) = 4/81.
Hence, option 'A' is the correct answer.
To find the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, we need to find the probability of getting the following results in four rolls:
- The minimum face value is 2, 3, 4, or 5
- The maximum face value is 2, 3, 4, or 5
Let's consider each of these separately.
Probability of minimum face value being 2, 3, 4, or 5:
- The probability of getting any one of these face values on a single roll is 4/6 = 2/3.
- Since we are rolling the die four times, the probability of getting any one of these face values on all four rolls is (2/3)^4 = 16/81.
- However, we need to consider all the possible ways in which these face values can occur in the four rolls. There are 4 possible positions for the minimum face value (first, second, third, or fourth roll), and for each position, there are 4 possible face values (2, 3, 4, or 5). Therefore, there are a total of 4x4 = 16 possible combinations of four rolls that satisfy the condition that the minimum face value is not less than 2.
- For each of these 16 combinations, the maximum face value can be any one of the 4 values 2, 3, 4, or 5, with equal probability. Therefore, the probability of getting a maximum face value that is not greater than 5, given that the minimum face value is not less than 2, is also 1/4.
- Therefore, the overall probability of getting a minimum face value that is not less than 2 and a maximum face value that is not greater than 5 is:
(16/81) x (1/4) = 4/81.
Hence, option 'A' is the correct answer.
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An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, isa)16/81b)1/81c)80/81d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, isa)16/81b)1/81c)80/81d)none of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, isa)16/81b)1/81c)80/81d)none of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unbaised die with faces marked 1,2,3,4,5 and 6 is rolled four times. Out of four face value obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, isa)16/81b)1/81c)80/81d)none of theseCorrect answer is option 'A'. Can you explain this answer?.
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