A lottery contains eight prizes and twenty blanks. If a lottery is randomly drawn, then what is the probability of getting a prize?1/82/52/71/5

1. Break Down the Problem

To find the probability of winning a prize in the lottery, we need to determine the total number of outcomes and the number of favorable outcomes.

• Total outcomes = Total prizes + Total blanks
• Favorable outcomes = Total prizes

2. Relevant Concepts

The probability $P$ of an event happening is given by the formula:

$P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

3. Analysis and Detail

1. Calculate the total number of outcomes:

   • Number of prizes = 8
   • Number of blanks = 20
   • Total outcomes = 8 + 20 = 28

2. Identify the number of favorable outcomes:

   • Favorable outcomes (prizes) = 8

3. Substitute the values into the probability formula: $P = \frac{8}{28}$

4. Simplify the fraction: $P = \frac{2}{7}$

4. Verify and Summarize

We have computed the total number of outcomes correctly and confirmed the number of favorable outcomes is accurate. The probability of drawing a prize in this lottery is $\frac{2}{7}$.

Final Answer

The probability of getting a prize is $\frac{2}{7}$.