Question

1. two hundred tickets are being sold for a school draw.

a) if you buy one ticket, what is your chance of winning, as a percent?
b) how many tickets would you need to purchase to have a 2.5% chance of winning?

Explanation:

Part (a)

Step 1: Define Probability

The probability of winning with one ticket is the number of winning tickets (1) divided by the total number of tickets (200). So the probability \( P=\frac{1}{200} \).

Step 2: Convert to Percentage

To convert a fraction to a percentage, multiply by 100. So \( P\times100=\frac{1}{200}\times100 \).
Simplify \( \frac{100}{200} = 0.5 \). So the percentage is \( 0.5\% \).

Step 1: Let the number of tickets be \( n \)

We know that the probability of winning is \( \frac{n}{200} \) (since there are 200 total tickets) and this probability is equal to \( 2.5\% \) or \( 0.025 \) in decimal form. So we set up the equation \( \frac{n}{200}=0.025 \).

Step 2: Solve for \( n \)

Multiply both sides of the equation by 200: \( n = 0.025\times200 \).
Calculate \( 0.025\times200 = 5 \).

Answer:

\( 0.5\% \)

Part (b)