A bag contains 12 identical pieces of paper, each of which has a different number from 1 to 12 written on it. If one of the pieces of paper is to be drawn from the bag at random, what is the probability that the number on this piece of paper will be divisible by 2 but not by 3?

Rationale

The probability that the number on the drawn piece of paper will be divisible by 2 but not by 3 is 04-Jan.

To determine this probability, we need to identify the numbers from 1 to 12 that meet the criteria of being divisible by 2 but not by 3. The valid numbers are 2, 4, 8, and 10, which gives us 4 favorable outcomes out of a total of 12.

A (12-Jan) YOUR ANSWER

This choice suggests that the probability is 12 out of 12, implying a certainty that any number drawn will meet the criteria. However, this is incorrect as not all numbers from 1 to 12 are divisible by 2 but not by 3. Thus, the actual favorable outcomes are limited to specific numbers.

B (04-Jan) CORRECT

This option accurately represents the correct probability as it indicates the fraction of favorable outcomes (4) over the total outcomes (12), simplifying to 1/3. This fraction reflects the numbers 2, 4, 8, and 10, which are divisible by 2 but not by 3.

C (03-Jan) YOUR ANSWER

This choice indicates a probability of 3 out of 12, which would suggest only three numbers meet the criteria. However, there are actually four numbers (2, 4, 8, 10) that satisfy being divisible by 2 and not by 3. Therefore, this option undercounts the favorable outcomes.

D (12-May) YOUR ANSWER

This selection inaccurately implies a probability of 12 out of 5, which is not a valid probability representation. Probabilities must be expressed as fractions between 0 and 1, making this choice nonsensical in the context of the question.

E (02-Jan) YOUR ANSWER

This choice implies a probability of 2 out of 12, which misrepresents the number of favorable outcomes. The accurate count of numbers divisible by 2 but not by 3 is four, not two, making this option incorrect.

Conclusion

The probability that a number drawn from the bag is divisible by 2 but not by 3 is correctly expressed as 04-Jan, indicating four suitable numbers (2, 4, 8, and 10) out of a total of twelve. This calculation ensures a clear understanding of the defined criteria and accurately quantifies the likelihood of such an outcome.

A bag contains 12 identical pieces of paper, each of which has a different number from 1 to 12 written on it. If one of the pieces of paper is to be drawn from the bag at random, what is the probability that the number on this piece of paper will be divisible by 2 but not by 3?

The probability that the number on the drawn piece of paper will be divisible by 2 but not by 3 is 04-Jan.

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