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Three identical dice are rolled. The probability that the same number will appear on each of them is
- a)1/36
- b)1/18
- c)1/6
- d)3/18
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Three identical dice are rolled. The probability that the same number ...
Solution:
Rolling of three identical dice is an example of independent events. The outcome of rolling one die is not affected by the outcome of rolling the other dice.
Probability of getting the same number on all three dice = Probability of getting a particular number on one die × Probability of getting the same number on the second die × Probability of getting the same number on the third die
Let the probability of getting a particular number (say 1) on one die be P(1). Since there are six possible outcomes on one die, P(1) = 1/6.
Therefore,
Probability of getting the same number on all three dice = P(1) × P(1) × P(1) = (1/6) × (1/6) × (1/6) = 1/216
However, the question asks for the probability of getting the same number on any of the three dice, not a particular number. Since there are six possible outcomes on one die, there are six possible outcomes that satisfy the condition of getting the same number on any of the three dice.
Therefore,
Probability of getting the same number on any of the three dice = 6 × (1/216) = 1/36
Hence, the correct option is (a) 1/36.
Rolling of three identical dice is an example of independent events. The outcome of rolling one die is not affected by the outcome of rolling the other dice.
Probability of getting the same number on all three dice = Probability of getting a particular number on one die × Probability of getting the same number on the second die × Probability of getting the same number on the third die
Let the probability of getting a particular number (say 1) on one die be P(1). Since there are six possible outcomes on one die, P(1) = 1/6.
Therefore,
Probability of getting the same number on all three dice = P(1) × P(1) × P(1) = (1/6) × (1/6) × (1/6) = 1/216
However, the question asks for the probability of getting the same number on any of the three dice, not a particular number. Since there are six possible outcomes on one die, there are six possible outcomes that satisfy the condition of getting the same number on any of the three dice.
Therefore,
Probability of getting the same number on any of the three dice = 6 × (1/216) = 1/36
Hence, the correct option is (a) 1/36.
Community Answer
Three identical dice are rolled. The probability that the same number ...
Total no of outcomes=6*6*6=216
fav outcomes =6 {(1,1,1)(2,2,2)(3,3,3)(4,4,4)(5,5,5)(6,6,6)
probability=6/216
=1/36
fav outcomes =6 {(1,1,1)(2,2,2)(3,3,3)(4,4,4)(5,5,5)(6,6,6)
probability=6/216
=1/36
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Three identical dice are rolled. The probability that the same number will appear on each of them isa)1/36b)1/18c)1/6d)3/18Correct answer is option 'A'. 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 Three identical dice are rolled. The probability that the same number will appear on each of them isa)1/36b)1/18c)1/6d)3/18Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical dice are rolled. The probability that the same number will appear on each of them isa)1/36b)1/18c)1/6d)3/18Correct answer is option 'A'. Can you explain this answer?.
Three identical dice are rolled. The probability that the same number will appear on each of them isa)1/36b)1/18c)1/6d)3/18Correct answer is option 'A'. 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 Three identical dice are rolled. The probability that the same number will appear on each of them isa)1/36b)1/18c)1/6d)3/18Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical dice are rolled. The probability that the same number will appear on each of them isa)1/36b)1/18c)1/6d)3/18Correct answer is option 'A'. Can you explain this answer?.
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