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Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the drawn ticket contains a number, which is a multiple of 3 or 7?
- a)2/5
- b)13/10
- c)7/20
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Tickets numbered from 1 to 20 are mixed up together and then a ticket ...
Understanding the Problem
To find the probability that a randomly drawn ticket from numbers 1 to 20 is a multiple of 3 or 7, we will follow these steps:
Step 1: Identify the Total Outcomes
- The total number of tickets is 20 (numbered 1 to 20).
Step 2: Find Multiples of 3
- The multiples of 3 from 1 to 20 are: 3, 6, 9, 12, 15, 18.
- Total multiples of 3 = 6.
Step 3: Find Multiples of 7
- The multiples of 7 from 1 to 20 are: 7, 14.
- Total multiples of 7 = 2.
Step 4: Find Common Multiples (Multiples of 21)
- The least common multiple of 3 and 7 is 21, which is greater than 20.
- Thus, there are no common multiples in this range.
Step 5: Calculate the Total Favorable Outcomes
- Total favorable outcomes = Multiples of 3 + Multiples of 7.
- Total favorable outcomes = 6 (multiples of 3) + 2 (multiples of 7) = 8.
Step 6: Calculate the Probability
- Probability (P) = Number of favorable outcomes / Total outcomes.
- P = 8 / 20 = 2 / 5.
Conclusion
The probability that the drawn ticket contains a number which is a multiple of 3 or 7 is 2/5. Thus, the correct answer is option 'A'.
To find the probability that a randomly drawn ticket from numbers 1 to 20 is a multiple of 3 or 7, we will follow these steps:
Step 1: Identify the Total Outcomes
- The total number of tickets is 20 (numbered 1 to 20).
Step 2: Find Multiples of 3
- The multiples of 3 from 1 to 20 are: 3, 6, 9, 12, 15, 18.
- Total multiples of 3 = 6.
Step 3: Find Multiples of 7
- The multiples of 7 from 1 to 20 are: 7, 14.
- Total multiples of 7 = 2.
Step 4: Find Common Multiples (Multiples of 21)
- The least common multiple of 3 and 7 is 21, which is greater than 20.
- Thus, there are no common multiples in this range.
Step 5: Calculate the Total Favorable Outcomes
- Total favorable outcomes = Multiples of 3 + Multiples of 7.
- Total favorable outcomes = 6 (multiples of 3) + 2 (multiples of 7) = 8.
Step 6: Calculate the Probability
- Probability (P) = Number of favorable outcomes / Total outcomes.
- P = 8 / 20 = 2 / 5.
Conclusion
The probability that the drawn ticket contains a number which is a multiple of 3 or 7 is 2/5. Thus, the correct answer is option 'A'.
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Community Answer
Tickets numbered from 1 to 20 are mixed up together and then a ticket ...
Favourable cases = 3, 6, 9, 12, 15, 18, 7, 14
Probability = 8/20 = 2/5
Probability = 8/20 = 2/5
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Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the drawn ticket contains a number, which is a multiple of 3 or 7?a)2/5b)13/10c)7/20d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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