SOLUTION: Find the probability on a single toss of a pair of six-sided dice of obtaining the different numbers on the two dice - (Enter your probability as a fraction.)

Algebra.Com
Question 1137450: Find the probability on a single toss of a pair of six-sided dice of obtaining the different numbers on the two dice - (Enter your probability as a fraction.)
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52905)   (Show Source): You can put this solution on YOUR website!
.

The space of events is the set of all pairs of integer numbers (i,j), where i and j are between 1 and 6, inclusively.


So, the set of events has 6*6 = 36 elements, all with the same probability of .


Of them, the favorable are those, where i and j are different: i =/= j.


The number of those with  i = j  is 6.


So, the favorable set consists of 36 - 6 = 30 elements.


Therefore, the probability under the question is  P =  = .

Solved.


Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!


There are often many different ways to solve probability problems. I like to solve any given problem by more than one method; getting the same answer by two different methods gives me confidence that I am interpreting and solving the problem correctly.

Here is a different method for solving this problem than shown by the other tutor.

Imagine rolling the dice one at a time, and find the probability that after each die you can still get the desired outcome (different numbers on the two dice).

On the first roll, you can get any number you want; that probability is 6/6 = 1.

On the second roll, you need to get a number different than on the first roll; that probability is 5/6.

So the probability of getting different numbers on the two dice is the product of those two probabilities: (1)*(5/6) = 5/6.
RELATED QUESTIONS

Find the probability on a single toss of a pair of dice of obtaining the following. (See... (answered by Fombitz)
Determine the probability of obtaining a total score of 3 or 4 on a single throw of two... (answered by Earlsdon)
In a single throw of a pair of dice;What is the probability of... (answered by Alan3354)
Suppose you roll a pair of six-sided dice. (a) What is the probability that the sum of (answered by ikleyn)
Consider Experiment of rolling a pair of six-sided dice. Suppose we are interested in the (answered by Edwin McCravy)
find probability of the sum 8 appears in a single toss of a pair of fair dice. (answered by ikleyn)
What is the probability of a toss of two dice giving a pair of identical... (answered by ikleyn)
In a single throw of a pair of dice, what is the probability that the obtaining a total... (answered by Edwin McCravy)
Two six-sided dice are rolled and the sum is recorded. Determine the probability of (answered by ikleyn)