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A number is drawn between 1 and 50, inclusive. What is the probability that a randomly selected number will not be a multiple of 5? Give your answer as a simplified fraction.

At least one is the complement of ______."

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Final answer:

The probability of randomly selecting a number between 1 and 50 that is not a multiple of 5 is 4/5. This is found by identifying the 10 multiples of 5 within the range and using the concept of complementary events to calculate the probability of the complementary event (not selecting a multiple of 5).

Step-by-step explanation:

The question asks about the probability that a randomly selected number from 1 to 50 is not a multiple of 5. To find this probability, we first identify the multiples of 5 between 1 and 50. These are 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. There are 10 multiples of 5 within this range.

Since there are 50 numbers in total, the probability of picking a multiple of 5 is 10/50, which simplifies to 1/5. To find the probability of not picking a multiple of 5, we find the complement of this event. The complement of an event occurring is 1 minus the probability of the event occurring, hence the probability of not picking a multiple of 5 is 1 - 1/5, which simplifies to 4/5.

Therefore, the answer to the question is that the probability of randomly selecting a number between 1 and 50 that is not a multiple of 5 is 4/5. This calculation uses the concept of complementary events, which is a crucial idea in probability. The sentence 'At least one is the complement of ______' would be completed by saying that 'at least one is the complement of none.'

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