Question

Meena calculates that the probability of her winning the first prize in a lottery is $0.08$. If total $800$ tickets were sold, the number of tickets bought by her, is

• A. $64$
• B. $640$
• C. $100$
• D. $10$

Hint:

To multiply a decimal by a multiple of 100, move the decimal point two places to the right and multiply by the remaining single digit:
\[ 0.08 \times 800 = 8 \times 8 = 64 \]

Answer 1

The Correct Option is A

Step 1: Write probability as a fraction of tickets.
Probability of winning = number of tickets Meena bought divided by the total tickets sold, i.e. $P = \frac{x}{800}$.
Step 2: Convert the decimal probability to a fraction.
\[ 0.08 = \frac{8}{100} = \frac{2}{25} \]
Step 3: Solve for $x$ using the fraction form.
\[ \frac{x}{800} = \frac{2}{25} \implies x = \frac{2}{25} \times 800 = 2 \times 32 \]
\[ x = 64 \]
Step 4: Conclude.
Meena bought 64 tickets, matching option (1).
\[ \boxed{64} \]