Is the product odd? 2

Probability Level 3

You randomly choose $2$ distinct positive integers between $1$ and $100$ inclusive. What is the probability that the product of both of their factors is odd?

Example: Say you took $17$ and $22$ . Factor of $17$ are $1, 17$ . Their product is $17$ which is odd. Factor of $22$ is $1, 2, 11, 22$ . Their product is $484$ . So, this is a fail. Should we have taken $23$ instead of $22$ , Both of the products would have been odd.

0

\frac12

\frac14

\frac2{33}

\frac{49}{198}

None of the above

1 solution

Saad Khondoker
Mar 9, 2021

The factors of even number have at least $1$ even number among them so the product of the factors of any even number is even.

The factors of odd number does not have any even number in it. So the product of the factors of any odd number is odd.

So, this has become a classic problem, what is the probability of taking $2$ (different) even numbers from $1st$ $100$ Natural numbers.

The probability is $^{50}C_{2}/^{100}C_{2}=49/198$

Doesn't this depend on considering 0 as a natural number? If you consider the natural numbers to be only positive integers, then the answer would be 25/99. You should probably have mentioned that zero is included.

Tristan Goodman - 3 months ago

There were some problem with the statement. I meant number 1 to 100 but wrote something else. I changed the statement. Thanks.

Saad Khondoker - 3 months ago

Is the product odd? 2

1 solution

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