Dice roll rule of sum

Probability Level 1

A fair 20-sided dice is rolled.

What is the probability that the roll is an even number or prime number or both?

Image Credit : Wikimedia Clément Bucco-Lechat .

\dfrac{2}{5}

\dfrac{1}{2}

\dfrac{17}{20}

\dfrac{9}{10}

2 solutions

Andy Hayes
May 31, 2016

Relevant wiki: Probability - Rule of Sum

There are $10$ even numbers on the 20-sided dice: $2,4,6,8,10,12,14,16,18,20$

There are $8$ prime numbers on the 20-sided dice: $2,3,5,7,11,13,17,19$

There is $1$ number that is both even and prime: $2$

By the rule of sum, the probability that an even or prime number is rolled is $\dfrac{10}{20}+\dfrac{8}{20}-\dfrac{1}{20}=\boxed{\dfrac{17}{20}}$

Didn't the question ask the probability of an even number or prime number or both? So both included?

Nancy Owen - 4 years ago

They are both included, but the number 2 is in both sets (2 is both even and prime).

Andy Hayes - 4 years ago

How come 1 is not included in the set of prime numbers for the 20-sided die?

shyam Vasanjee - 2 years, 5 months ago

1 is not prime by definition. It is one of those interesting 'math facts' that could have gone many ways. Because definition of prime requires divisibility by 2 numbers, 1 and itself, 1 is excluded as it is only divisible by one number. Outside of the prime thing, I like to talk about the magic of 1 in math.

Drew Professional - 2 years ago

If I wanted to calculate even number or prime number (so exclusive or), I would get 10/20 + 8/20 - 2* 1/20 = 16/20 right?

Stephan S - 2 years, 4 months ago

prime number :a number that is divisible only by itself and 1

Ismael Moha - 2 years, 1 month ago

and also the condition that the two numbers it is divisible by are different, so 1 does not count :)

Dimitar Kalmadanski - 2 months ago

Hesham Haikal
Sep 15, 2018

It is easier in this case to think of remaining odd numbers that are not prime in which are: ${ 1, 9, 15 }$

Therefore the probability of an even number or prime number has rolled is $\frac{20 - 3}{20}$ = $\frac{17}{20}$

Working Backwards is sometimes hugely rewarding.

Aniruddha Bagchi - 2 years ago

Dice roll rule of sum

Image Credit : Wikimedia Clément Bucco-Lechat .

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