In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

Question

In a lottery there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

1. A. 1/11
2. B. 2/15
3. C. 2/7 (Correct answer)
4. D. 1/14

Correct Answer

Option C — 2/7

Detailed Solution & Explanation

The correct answer is 2/7.

Key Points

• This tests basic probability: the chance of a favourable outcome equals favourable cases divided by total cases.
• Probability = (Number of favourable outcomes) ÷ (Total number of outcomes).
• There are 10 prizes and 25 blanks, so the total number of tickets = 10 + 25 = 35.
• A prize is the favourable outcome, so:
• P(prize) = 10 ÷ 35 = 2/7.
• always compute the total sample space first (prizes + blanks), a step candidates skip by using 10/25. Probability is a fraction between 0 and 1; here 2/7 ≈ 0.286.

Exam Tip

• the probability of not winning (getting a blank) would be 25/35 = 5/7, and note that P(prize) + P(blank) = 2/7 + 5/7 = 1, a quick way to confirm your answer.