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A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 < />2 < />3 < />4 < />5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)
Correct answer is '0.075'. Can you explain this answer?
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Understanding the Problem
To calculate the probability that the fourth drawn ticket (t4) is 25 when selecting 5 tickets from a bag of 30 numbered tickets, we need to consider how the tickets can be arranged.
Total Combinations
- The total number of ways to choose 5 tickets from 30 is given by the combination formula:
\[
C(30, 5) = \frac{30!}{5!(30-5)!} = 142506
\]
Favorable Outcomes for t4 = 25
- For t4 to be exactly 25, we must choose:
- 3 tickets from the numbers below 25 (i.e., from 1 to 24).
- 1 ticket from the numbers above 25 (i.e., from 26 to 30).
- The number of ways to choose 3 tickets from the 24 tickets below 25 is:
\[
C(24, 3) = \frac{24!}{3!(24-3)!} = 2024
\]
- The number of ways to choose 1 ticket from the 5 tickets above 25 is:
\[
C(5, 1) = 5
\]
Calculating Favorable Combinations
- The total favorable combinations where t4 is 25:
\[
\text{Favorable Outcomes} = C(24, 3) \times C(5, 1) = 2024 \times 5 = 10120
\]
Calculating the Probability
- The probability of t4 being 25 is then calculated as follows:
\[
P(t4 = 25) = \frac{\text{Favorable Outcomes}}{\text{Total Combinations}} = \frac{10120}{142506} \approx 0.071
\]
- Rounding to three decimal places, we find:
\[
P(t4 = 25) \approx 0.075
\]
Conclusion
- Therefore, the probability of t4 being 25 is approximately **0.075**.
To calculate the probability that the fourth drawn ticket (t4) is 25 when selecting 5 tickets from a bag of 30 numbered tickets, we need to consider how the tickets can be arranged.
Total Combinations
- The total number of ways to choose 5 tickets from 30 is given by the combination formula:
\[
C(30, 5) = \frac{30!}{5!(30-5)!} = 142506
\]
Favorable Outcomes for t4 = 25
- For t4 to be exactly 25, we must choose:
- 3 tickets from the numbers below 25 (i.e., from 1 to 24).
- 1 ticket from the numbers above 25 (i.e., from 26 to 30).
- The number of ways to choose 3 tickets from the 24 tickets below 25 is:
\[
C(24, 3) = \frac{24!}{3!(24-3)!} = 2024
\]
- The number of ways to choose 1 ticket from the 5 tickets above 25 is:
\[
C(5, 1) = 5
\]
Calculating Favorable Combinations
- The total favorable combinations where t4 is 25:
\[
\text{Favorable Outcomes} = C(24, 3) \times C(5, 1) = 2024 \times 5 = 10120
\]
Calculating the Probability
- The probability of t4 being 25 is then calculated as follows:
\[
P(t4 = 25) = \frac{\text{Favorable Outcomes}}{\text{Total Combinations}} = \frac{10120}{142506} \approx 0.071
\]
- Rounding to three decimal places, we find:
\[
P(t4 = 25) \approx 0.075
\]
Conclusion
- Therefore, the probability of t4 being 25 is approximately **0.075**.
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A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer?
Question Description
A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer?.
A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer?.
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A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer?, a detailed solution for A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer? has been provided alongside types of A bag contains 30 tickets numbered 1,2,3, ......... up to 30. Among them 5 are drawn at random and arranged in ascending order t1 2 3 4 5. The probability of t4 being 25 (Up to two decimal places) is . (Up to three decimal places)Correct answer is '0.075'. Can you explain this answer? theory, EduRev gives you an
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