Question

Tom sold 100 lottery tickets in which 5 tickets carry prizes. If Jerry purchased a ticket, what is the probability of Jerry winning a prize? (1) \(\frac{19}{20}\) (2) \(\frac{1}{25}\) (3) \(\frac{1}{20}\) (4) \(\frac{17}{20}\)

Short answer

Answer: (3) \(\frac{1}{20}\)

Step-by-step solution

Understand the problem

There are 100 lottery tickets, 5 of which carry prizes. We want to find the probability of Jerry winning a prize with one purchased ticket.

Calculate the probability of winning

Since 5 out of 100 tickets carry prizes, we can use the simple probability formula to find the probability of Jerry winning a prize: Probability of winning \(= \frac{\text{Number of successful outcomes}}{\text{Total number of possible outcomes}} = \frac{5}{100}\).

Simplify the fraction

To simplify the fraction \(\frac{5}{100}\), we divide the numerator and the denominator by 5: \(\frac{5}{100} = \frac{1}{20}\)

Find the answer in the options

Now that we have the probability of Jerry winning a prize, we can look for the answer in the given options. The correct answer is (3) \(\frac{1}{20}\).

Key concepts

Lottery

Lotteries have always been a thrilling concept for individuals hoping for a chance to win a prize. A lottery involves purchasing a ticket that enters you into a pool of other tickets. Each ticket represents a chance to win. In essence, the fewer the tickets that carry a prize, the lesser the probability of winning. Lotteries play on chance and randomness; however, they follow the simple rules of probability which allow participants to calculate the likelihood of winning. This calculation forms the basic understanding of probability in lottery structures, making it an interesting and practical application of mathematics.

Fraction Simplification

Simplifying fractions is an essential skill in mathematics, making complex problems easier to understand and solve. When you simplify a fraction, you divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor. For example, if you have a fraction like \( \frac{5}{100} \), you simplify it by dividing both 5 and 100 by 5. This gives you \( \frac{1}{20} \). Simplification is crucial because it allows you to present the most concise and easiest-to-understand form of a fraction, which is particularly helpful in identifying accurate probabilities and comparing different outcomes.

Successful Outcomes

In the context of probability, a successful outcome is an event that meets the conditions specified by the problem. In lottery problems, a successful outcome would be purchasing a ticket that wins a prize. When calculating probability, the number of successful outcomes is the first step in the process, crucial for forming a clear picture of the odds. In our problem, there are 5 successful outcomes, as 5 tickets out of 100 will win a prize. Thus, the probability of a successful outcome, which is winning, is \( \frac{5}{100} \). Knowing how to define and count successful outcomes helps in computing probabilities correctly.

Mathematics Class 8

At the Mathematics Class 8 level, students are introduced to probability, a fundamental concept that applies to various real-world scenarios. Probabilities are expressed as fractions or percentages, representing the likelihood of different outcomes. Learning probability helps students develop critical thinking and analytical skills. They understand that probability is about predicting the chance of events. In our example, students calculate the probability of Jerry winning a prize by dividing the number of prize-winning tickets by the total number of tickets. It's a simple yet powerful way to make predictions about likely occurrences, prepared by understanding each step precisely.