Question

A. How many integers from 1 through 1,000 are multiples of 4 or multiples of 3?

B. Suppose an integer from 1 through 1,000 is chosen at random. Use the result of part (a) to find the probability that the integer is a multiple of 4 or a multiple of 3. (Round to the nearest tenth of a percent.)

C. How many integers from 1 through 1,000 are neither multiples of 4 nor multiples of 3?

Answer 1

A) Number of multiples of 4 = 1000/4 = 250

Number of multiples of 3 = 1000/3 = 333.33

We will only consider the interger portion of the number. So, number of multiples of 3 are 333.

There will be numbers which are multiples if both 3 and 4 and have been double counted and we need to subtract them.

So, number of multiples of (3*4 = 12) = 1000/12

= 83.33.

We will consider only the integer portion, which is 83.

So, the total number of integers that are multiples of 3 or 4 = 250+333-83 = 500

B) Probability that a randomly chosen number is a multiple of 3 or 4 = 500/1000 = 0.5

C) Number of integers between 1 to 1000, that are neither multiples of 3, nor the multiples of 4 are =

1000 - Number of integers that are multiple of 3 or 4

= 1000 - 500

= 500.

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