What is the probability that the same number will be facing up on each of three standard six-sided dice that are tossed simultaneously? Express your answer as a common fraction.

Swim2433 Jul 25, 2020

#1**0 **

First die =any number =6/6

2nd die - The probability that it is different from the first die = 5/6

3rd die - The probability that it is different from the first two= 4/6

Then, the probability that ALL three are different from each other =6/6 x 5/6 x 4/6 =120 / 216

Then, the probability that ALL three show the same number **= 1 - 120 / 216 = 96 / 216 = 4 / 9**

Guest Jul 25, 2020

#2**+1 **

216 possible rolls

6 rolls will fit the criteria 666 555 444 333 222 111

6 /216 = 1/36 chance

ElectricPavlov Jul 25, 2020

#3**0 **

(1) The first die can be anything.

(2) The odds of the second die being the same as the first = 1/6

(3) The odds of the third die being the same as the first = 1/6

1 1 **1**

The odds of both (2) and (3) happening = –– x –– = **—–**

6 6 **36**

_{.}

Guest Jul 25, 2020