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Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3 ?
- a)3/10
- b)3/20
- c)2/5
- d)1/2
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at ra...
Here, S = {1, 2, 3, 4,........, 19, 20}
Let E = even of getting a multiple of 3 = {3, 6, 9, 12, 15, 18}
Let E = even of getting a multiple of 3 = {3, 6, 9, 12, 15, 18}
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Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at ra...
Understanding the Problem
To find the probability that a randomly drawn ticket from a set of tickets numbered 1 to 20 is a multiple of 3, we need to follow a systematic approach.
Step 1: Identify the Total Number of Outcomes
- The tickets are numbered from 1 to 20.
- Therefore, the total number of possible outcomes is 20.
Step 2: Identify the Favorable Outcomes
- We need to count how many tickets are multiples of 3 within this range.
- The multiples of 3 between 1 and 20 are: 3, 6, 9, 12, 15, and 18.
Step 3: Count the Favorable Outcomes
- Listing the multiples:
- 3
- 6
- 9
- 12
- 15
- 18
- There are a total of 6 favorable outcomes.
Step 4: Calculate the Probability
- The probability (P) of drawing a ticket that is a multiple of 3 is given by the formula:
P = (Number of Favorable Outcomes) / (Total Number of Outcomes)
- Substituting the values:
P = 6 / 20
Step 5: Simplify the Probability
- This can be simplified to:
P = 3 / 10
Conclusion
- Therefore, the probability that the ticket drawn bears a number which is a multiple of 3 is 3/10.
- Hence, the correct answer is option 'A'.
To find the probability that a randomly drawn ticket from a set of tickets numbered 1 to 20 is a multiple of 3, we need to follow a systematic approach.
Step 1: Identify the Total Number of Outcomes
- The tickets are numbered from 1 to 20.
- Therefore, the total number of possible outcomes is 20.
Step 2: Identify the Favorable Outcomes
- We need to count how many tickets are multiples of 3 within this range.
- The multiples of 3 between 1 and 20 are: 3, 6, 9, 12, 15, and 18.
Step 3: Count the Favorable Outcomes
- Listing the multiples:
- 3
- 6
- 9
- 12
- 15
- 18
- There are a total of 6 favorable outcomes.
Step 4: Calculate the Probability
- The probability (P) of drawing a ticket that is a multiple of 3 is given by the formula:
P = (Number of Favorable Outcomes) / (Total Number of Outcomes)
- Substituting the values:
P = 6 / 20
Step 5: Simplify the Probability
- This can be simplified to:
P = 3 / 10
Conclusion
- Therefore, the probability that the ticket drawn bears a number which is a multiple of 3 is 3/10.
- Hence, the correct answer is option 'A'.
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Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3 ?a)3/10b)3/20c)2/5d)1/2Correct answer is option 'A'. Can you explain this answer?
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