Ben rolls four fair 20-sided dice, and each of the dice has faces numbered from 1 to 20. What is the probability that exactly two of the dice show an even number?

Guest Dec 11, 2017

#1**+1 **

Each 20-sided die has 10 odd-numbered sides and 10 even-numbered sides.

To show exactly two even numbers, you must also show two odd numbers.

The probability of showing an even number is 1/2; the probability of showing an odd number is also 1/2.

There are 6 combinations that show two even numbers and two odd numbers:

6 x (1/2)^{2} x (1/2)^{2} = 6/16 = 3/8

geno3141
Dec 11, 2017

#2**+1 **

Melody: Please adjudicate the right answer between the above by "geno3141" and this by "CPhill":

**http://web2.0calc.com/questions/please-help-asap_10**

Thank you.

Guest Dec 11, 2017

#3**+2 **

Hi Guest, certainly I will adjudicate :)

I'd like you to become a member so next time I will know who you are. I'd like that a lot

Gino's answer is correct, CPhill just misread the question.

Ben rolls four fair 20-sided dice, and each of the dice has faces numbered from 1 to 20. What is the probability that exactly two of the dice show an even number?

This is the same as rolling a die 4 times, it doesn't matter that there are 20 sides, becasue we only care whether the roll is even or odd.

The probability of any individual roll being even (sucess) is 0.5 and

The probability of any individual roll being odd (failure) is 0.5

You want exactly 2 even and therfore 2 odd rolls

P(exactly 2 successes)

=[ number of ways 2 items can be chosen from 4] * [prob of success^2] * [ prob of failure^2]

= 4C2 * (1/2)^2 * (1/2)^2

= 6 * 1/4 * 1/4

= 6/16

= 3/8

Melody
Dec 11, 2017

#4**+1 **

This is Mr. BB. He probably wonâ€™t be signing up anytime soon.

However, when he does decide to sign up, he can ** adjudicate **an appropriate name from this list of great and applicable user names. Most should still be available. Only the most elite of members are entitled to them.

GingerAle
Dec 13, 2017