+83 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.
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
+37159 216 possible rolls
6 rolls will fit the criteria 666 555 444 333 222 111
6 /216 = 1/36 chance
(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
.
