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Q: 260 divisible by 10

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Assuming a standard unbiased 6-sided die: The probability of 5 or 3 = 2/6 = 1/3 → The expectation when it is rolled 260 times is 260 × 1/3 = 86 2/3 → You would expect to see a 5 or 3 about 87 times when rolling a die 260 times

AnswerThe probability that a randomly chosen [counting] number is not divisible by 2 is (1-1/2) or 0.5. One out of two numbers is divisible by two, so 1-1/2 are not divisible by two.The probability that a randomly chosen [counting] number is not divisible by 3 is (1-1/3) = 2/3.Similarly, the probability that a randomly chosen [counting] number is not divisible by N is (1-1/N).The probability that a random number is not divisible by any of 2, 3 or 6 can be reduced to whether it is divisible by 2 or 3 (since any number divisible by 6 can definitely be divided by both and so it is irrelevant). This probability depends on the range of numbers available. For example, if the range is all whole numbers from 0 to 10 inclusive, the probability is 3/11, because only the integers 1, 5, and 7 in this range are not divisible by 2, 3, or 6. If the range is shortened, say just from 0 to 1, the probability is 1/2.Usually questions of this sort invite you to contemplate what happens as the sampling range gets bigger and bigger. For a very large range (consisting of all integers between two values), about half the numbers are divisible by two and half are not. Of those that are not, only about one third are divisible by 3; the other two-thirds are not. That leaves 2/3 * 1/2 = 1/3 of them all. As already remarked, a number not divisible by two and not divisible by three cannot be divisible by six, so we're done: the limiting probability equals 1/3. (This argument can be made rigorous by showing that the probability differs from 1/3 by an amount that is bounded by the reciprocal of the length of the range from which you are sampling. As the length grows arbitrarily large, its reciprocal goes to zero.)This is an example of the use of the inclusion-exclusion formula, which relates the probabilities of four events A, B, (AandB), and (AorB). It goes like this:P(AorB) = P(A) + P(B) - P(AandB)In this example, A is the event "divisible by 2", and B is the event "divisible by 3".

No, 120 is not the smallest number that is divisible by 1,2,3,4,5 and 6.

As you might have already figured out, you have to count every 2nd number! For example, it goes a little something like this: 10 45 80 and 125, and the second number line is 30 40 50 and 60. So that means, in the next 8 numbers, the pattern goes like this: 10 30 45 40 80 50 125 60 160 70 205 80 260 90 315 and 100!

2/6 or 1/3

Related questions

No, 4 is smaller than 260. But 260 is divisible by 4.

It is divisible by 2.

Is it divisible

No.

The number 1,260 is divisible by 2, 3, 4, 5, 6, 9, and 10.

1, 2, 5, 10, 13, 26, 65, 130

All multiples of 260 (which are infinite) including 260, 520, 780, 1040, 1300 . . .

260

260

Just multiply 260 by numbers: 520 (2x), 780 (3x), etc.

Yes, 520 / 2 = 260

26

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