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A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each is
- a)1/46656
- b)1/5184
- c)5/11664
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly...
Understanding the Problem
When rolling a dice 6 times, we want to find the probability of getting the numbers 2 and 4 exactly three times each.
Defining the Scenario
- We have a total of 6 rolls.
- We need to get 2 three times and 4 three times.
- The remaining outcomes can be any of the other four faces (1, 3, 5, 6), which we do not care about.
Calculating the Probability
1. Ways to Choose Positions:
- The number of ways to choose 3 positions for the number 2 from 6 rolls is given by the combination formula:
\[
\binom{6}{3} = 20
\]
- The remaining positions (3 of them) will automatically be for the number 4.
2. Calculating the Outcomes:
- For the other three rolls, each can be any of the faces 1, 3, 5, or 6. Hence, there are:
\[
4^0 = 1 \quad \text{(Since we don't want any of these numbers)}
\]
3. Total Outcomes:
- The total possible outcomes when rolling a dice 6 times is:
\[
6^6 = 46656
\]
4. Probability Calculation:
- Therefore, the probability \( P \) is calculated as:
\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{20 \cdot 1}{46656} = \frac{20}{46656}
\]
5. Final Probability:
- Simplifying \( \frac{20}{46656} \) gives:
\[
\frac{5}{11664}
\]
Conclusion
Thus, the correct answer is option 'C' \( \frac{5}{11664} \).
When rolling a dice 6 times, we want to find the probability of getting the numbers 2 and 4 exactly three times each.
Defining the Scenario
- We have a total of 6 rolls.
- We need to get 2 three times and 4 three times.
- The remaining outcomes can be any of the other four faces (1, 3, 5, 6), which we do not care about.
Calculating the Probability
1. Ways to Choose Positions:
- The number of ways to choose 3 positions for the number 2 from 6 rolls is given by the combination formula:
\[
\binom{6}{3} = 20
\]
- The remaining positions (3 of them) will automatically be for the number 4.
2. Calculating the Outcomes:
- For the other three rolls, each can be any of the faces 1, 3, 5, or 6. Hence, there are:
\[
4^0 = 1 \quad \text{(Since we don't want any of these numbers)}
\]
3. Total Outcomes:
- The total possible outcomes when rolling a dice 6 times is:
\[
6^6 = 46656
\]
4. Probability Calculation:
- Therefore, the probability \( P \) is calculated as:
\[
P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{20 \cdot 1}{46656} = \frac{20}{46656}
\]
5. Final Probability:
- Simplifying \( \frac{20}{46656} \) gives:
\[
\frac{5}{11664}
\]
Conclusion
Thus, the correct answer is option 'C' \( \frac{5}{11664} \).
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A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each isa)1/46656b)1/5184c)5/11664d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each isa)1/46656b)1/5184c)5/11664d)none of theseCorrect answer is option 'C'. 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 A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each isa)1/46656b)1/5184c)5/11664d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each isa)1/46656b)1/5184c)5/11664d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each isa)1/46656b)1/5184c)5/11664d)none of theseCorrect answer is option 'C'. 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 A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each isa)1/46656b)1/5184c)5/11664d)none of theseCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A dice is rolled 6 times. The probability of obtaining 2 and 4 exactly three times each isa)1/46656b)1/5184c)5/11664d)none of theseCorrect answer is option 'C'. Can you explain this answer?.
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