Multiple choice

An urn contains 6 red, 4 blue, 2 green and 3 yellow marbles. If four marbles are picked at random, then what is the probability that at least one is blue?

  1. 4 19

  2. 69 91

  3. 11 15

  4. 22 91

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

Total marbles = 15. Probability of picking no blue marbles in 4 draws is (11/15) * (10/14) * (9/13) * (8/12) = 22/91. The probability of at least one blue is 1 - 22/91 = 69/91.

AI explanation

Using the complementary event method, the total number of marbles is 15 and the total ways to pick 4 marbles is 15C4, which equals 1365. The non-blue marbles account for 11, so the ways to pick 4 non-blue marbles is 11C4, which equals 330. The probability of picking at least one blue is 1 minus 330 divided by 1365, resulting in 69/91.

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