how many integers from 1 to 600 are divisible by 2 or 3?

Question

b) find the probability that a random integar from 1 to 600 is divisible by neither 2 nor 3



thanks

Answer 1

by 2 300 all even numbers

by 3 600/3 is 200 every third one

divisable by niether
300 odd, every third odd is divisable by three so 200
200/600
1/3
33.3%

Answer 2

Obviously, there's 200 integers divisible by 3, and 300 integers divisible by 2. But some of these numbers are divisible by 2 and 3, meaning they're divisible by 6. You'll have to figure out how many are divisible by 6 and subtract that number from the 200+300 to get the answer.

Answer 3

200 integers are divisible by 3. 300 integers are divisible by 2. However, there are integers that are divisible by both. Of the 200 integers divisible by 3, 100 are also divisible by 2. Thus, the integers divisible by either 2 or 3 (or both) is 400. Thus 1/3 are divisible by neither.

Answer 4

300 are divisible by 2.

200 are divisible by 3.

That leaves 100, but 100 are divisible by both 2 and 3. So, subtract 100 to account for the dupes, and you have 400.

The second question is just the opposite of the first, so 600 - 400 = 200

Answer 5

1 - P(#s divisible by 2 or 3)
1 - (P(#divisible by 2) + P(#divisible by 3) - P(#divisible by both)
1 - (1/2 + 1/3 - 1/6)
= 2/6 = 1/3

Answer 6

All the multiples of 6 are divisible for 2 and 3.
M(6) = {6, 12, 18, ... 600}
an = a1 + (n - 1)6
600 = 6 + 6n - 6
600 = 6n
n = 600 / 6
n = 100
Answer: There are 100 integers.
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Answer 7

All of them are divisible by 2 or 3

most of the prime numbers are not divisible by 2 and 3. (2 and 3 are)

Answer 8

300 are divisible by 2.

200 are divisible by 3.

That makes 500.

Now subtract the number divisible by six (100)since they were counted twice and you have 400.