Multiple choice

Directions: An urn has 6 red marbles, 8 green marbles and 11 blue marbles. Three marbles are drawn. What is the probability that at least one of them is green?

  1. 34/115

  2. 81/115

  3. 14/575

  4. 91/115

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total marbles = 6+8+11 = 25. Probability of no green = (17/25) * (16/24) * (15/23) = (17/25) * (2/3) * (15/23) = (17 * 2 * 5) / (25 * 23) = 170 / 575 = 34/115. Probability of at least one green = 1 - 34/115 = 81/115.

AI explanation

To find the probability of at least one green marble, we use the complement rule, calculating 1 minus the probability of drawing no green marbles. The urn contains 6 red and 11 blue marbles, meaning 17 are not green, out of 25 total marbles. The probability of drawing 3 non-green marbles from the 17 available is calculated using combinations as 17C3 divided by 25C3, which simplifies to 34/115. Subtracting this from 1 gives 1 minus 34/115, resulting in 81/115.

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