Calculating Probabilities in a Random Ticket Draw

A common problem in probability theory involves determining the likelihood of drawing a ticket with specific characteristics from a bag containing a set of tickets. This article explores the probability of drawing a ticket that meets certain criteria. Specifically, we will calculate the probability of drawing a ticket that is a multiple of 2, 3, 4, 7, or 5 from a set of 20 tickets numbered from 1 to 20.

Understanding the Problem

The problem statement specifies a bag of 20 tickets marked with the numbers 1 to 20. We need to determine the probability of drawing a ticket that is a multiple of 2, 3, 4, 7, or 5. The original problem had some typographical errors, which we will correct in this explanation. The corrected problem involves multiples of 2, 3, 4, 7, and 5.

Step 1: List the Multiples

We start by listing all the tickets that are multiples of the specified numbers.

Multiples of 2

2, 4, 6, 8, 10, 12, 14, 16, 18, 20

There are 10 multiples of 2 in the range from 1 to 20.

Multiples of 3

3, 6, 9, 12, 15, 18

There are 6 multiples of 3 in the range from 1 to 20.

Multiples of 4

4, 8, 12, 16, 20

There are 5 multiples of 4 in the range from 1 to 20.

Multiples of 7

7, 14

There are 2 multiples of 7 in the range from 1 to 20.

Multiples of 5

5, 10, 15, 20

There are 4 multiples of 5 in the range from 1 to 20.

Step 2: Combine the Information

To find the total number of favorable outcomes, we combine the multiples while avoiding double-counting. The combined multples are:

2, 4, 6, 8, 10, 12, 14, 15, 16, 18, 20

This set contains 11 unique numbers. However, since 16 and 20 are counted twice, we correct the count as follows:

2, 4, 6, 8, 10, 12, 14, 15, 16, 18 These are the 10 unique numbers plus 20, making it 11 unique numbers.

Thus, the total number of favorable outcomes is 10 1 11.

Step 3: Calculate the Probability

The probability of drawing a ticket that is a multiple of 2, 3, 4, 7, or 5 is given by the ratio of the number of favorable outcomes to the total number of outcomes.

Probability (frac{10 1}{20} frac{11}{20})

Conclusion

The probability of drawing a ticket that is a multiple of 2, 3, 4, 7, or 5 from a set of 20 tickets numbered from 1 to 20 is (frac{11}{20}) or 0.55.

Related Articles and Keywords

This topic relates closely to the concepts of probability, multiples, and random draws. Understanding these concepts can help in solving similar problems and furthering your knowledge in probability theory. The key terms to remember include probability, multiple, and random draw.