A box contains 10 red, 5 green, and 10 blue marbles. A marble is chosen at random from the box, and it is noted that it is not one of the blue marbles. What is the probability that it is green?

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BlackTom AI · Accepted Answer

Start by parsing the scenario: the box contains 10 red, 5 green, and 10 blue marbles, totaling 25 marbles. We are told the marble drawn is not blue, so we are effectively choosing from the non-blue marbles only.

First, determine the relevant sample space given the condition. The non-blue marbles consist of 10 red and 5 green, for a total of 15 marbles. This is the set from which the observed marble could have come.

Next, focus on the event of interest within that restricted sample space: drawing a green marble. There are 5 green marbles available in the non-blue group.

Compute the conditional probability: number of favorable green outcomes (5) divided by the size of the conditional sample space (15). That yields 5/15 = 1/3.

Now evaluate each option:
- Option a: None of these. This would only be true if none of the listed probabilities matched the scenario, but 1/3 is indeed achievable, so this is incorrect.
- Option b: 1/4. This would imply 25% probability, which does not align with the 5 green out of 15 non-blue ratio.
- Option c: 1/5. This would be 20%, also not matching the 5/15 calculation.
- Option d: 3/5. This is 60%, far from the calculated conditional probability.
- Option e: 1/3. This matches the computed conditional probability exactly, since 5 green out of 15 non-blue equals 1/3.

In summary, restricting to non-blue marbles changes the sample space to 15, and within that space the green portion is 5 out of 15, which simplifies to 1/3.

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A box contains 10 red, 5 green, and 10 blue marbles. A marble is chosen at random from the box, and it is noted that it is not one of the blue marbles. What is the probability that it is green?

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