How To Manufacture Such A Dice?

Probability Level 1

I have built a fair 101-sided dice. If I rolled the dice once, which of the following events is more likely to occur?

"I rolled an odd number." versus "I rolled an even number."

Clarification : Each face of the dice is labelled with a distinct integer in the interval 1 to 101 (inclusive).

I rolled an odd number I rolled an even number Both events are equally likely to occur

2 solutions

Pranshu Gaba
May 3, 2016

Since it is a fair dice, each number on the dice is equally like to occur. Since there are 101 faces on the dice, each face is equally likely to come up, with a probability of $\frac{1}{101}$ .

Out of the 101 faces, 51 are odd and 50 are even. Therefore, The probability of rolling an odd number is $\frac{51}{101}$ and the probability of rolling an even number is $\frac{50}{101}$ .

We see that the probability of rolling an odd number is greater, and therefore it is more likely to occur. $_\square$

Yup. The number of positive odd numbers less than a certain integer is not always equal to the number of positive even numbers less than that same integer. I've made that false assumption one too many times already.

Thank you for your solution ;)

Chung Kevin - 5 years, 1 month ago

William Whitehouse
May 12, 2016

I hate to be pedantic but rolling either will be impossible: If a face of the die if on the ground then it would have to have an even number of faces for one to be facing upwards.Still a good problem :)

How To Manufacture Such A Dice?

2 solutions

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