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.)
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-> 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.)
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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(52817) (Show Source):
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 = = .
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.
