Multiple choice

In a lottery game, there are 50 main numbered balls (1 to 50), and 6 balls are randomly drawn without replacement. Additionally, there are 10 special "bonus" balls numbered 1 to 10, and 1 bonus ball is drawn separately. What is the probability of matching all 6 main numbers ball and the bonus ball in the exact order they are drawn?

  1. 1/(50 × 49 × 48 × 47 × 46 × 45 × 10)

  2. (1 × 6)/(50 × 49 × 48 × 47 × 46 × 45 × 10)

  3. (10 × 6)/(50 × 49 × 48 × 47 × 46 × 45 × 10)

  4. (50 × 6)/(50 × 49 × 48 × 47 × 46 × 45 × 10)

  5. a
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since the balls must be matched in the exact order they are drawn, the probability of matching the first ball is 1/50, the second is 1/49, and so on, down to 1/45 for the sixth ball. The probability of matching the single bonus ball is 1/10, so the combined probability is the product of these individual probabilities.

AI explanation

To match the exact order of the 6 main balls drawn without replacement, the probability is the product of the individual probabilities for each step: 1/50 times 1/49 times 1/48 times 1/47 times 1/46 times 1/45. The separate bonus ball has a 1/10 probability of being matched. Multiplying these together gives a total probability of 1/(50 times 49 times 48 times 47 times 46 times 45 times 10).

Keep practicing — related questions