A lottery has 20 prizes and 15 blanks (total 35 tickets). If one ticket is drawn at random, what is the probability of getting a prize?

Introduction / Context:We compute a basic probability from a finite set of equally likely outcomes. Each ticket is equally likely, and we count favourable outcomes (prizes).

Given Data / Assumptions:

• Prizes: 20, blanks: 15.
• Total tickets = 35.
• Single random draw.

Concept / Approach:Probability = favourable/total = 20/35. Reduce the fraction to simplest form.

Step-by-Step Solution:Favourable outcomes (prizes) = 20.Total outcomes = 35.Probability = 20/35 = 4/7 after dividing numerator and denominator by 5.

Verification / Alternative check:Compute P(blank) = 15/35 = 3/7. Then P(prize) = 1 − 3/7 = 4/7, consistent.

Why Other Options Are Wrong:1/10 and 2/7 are too small; 2/5 = 14/35 undercounts prizes.

Common Pitfalls:Not simplifying the fraction or mixing up the counts for prizes and blanks.

Final Answer:4/7