Multiple choice

A bag contains 10 black marbles, some red marbles and some green marbles. If the number of red marbles is 5 times the number of green marbles and twice the number of black marbles, then what is the probability of getting at least one red marble when two marbles are drawn from the bag?

  1. 480/531

  2. 470/561

  3. 460/501

  4. None of these

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Black = 10. Red = 2 * Black = 20. Red = 5 * Green, so Green = 4. Total = 34. Probability of no red = (14/34) * (13/33) = 182 / 1122 = 91 / 561. Probability of at least one red = 1 - (91/561) = 470/561.

AI explanation

Given 10 black marbles, the number of red marbles is twice this amount, giving 20 red marbles. The number of green marbles is found by dividing the red marbles by 5, yielding 4 green marbles, for a total of 34 marbles. The probability of getting no red marbles when drawing two is the combination of 14 non-red marbles taken two at a time divided by the combination of 34 taken two at a time, which is (14 times 13) divided by (34 times 33), equaling 91 out of 561. The probability of at least one red marble is 1 minus 91/561, leaving 470/561.

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