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Reika [66]
2 years ago
15

If two standard six-sided dice are tossed, what is the probability that a 5 is rolled on at least one of the two dice? express y

our answer as a common fraction.
Mathematics
1 answer:
zaharov [31]2 years ago
6 0
We define the probability of a particular event occurring as:
\frac{number\ of \ desired\ outcomes}{number\ of\ possible\ outcomes}

What are the total number of possible outcomes for the rolling of two dice? The rolls - though performed at the same time - are <em>independent</em>, which means one roll has no effect on the other. There are six possible outcomes for the first die, and for <em>each </em>of those, there are six possible outcomes for the second, for a total of 6 x 6 = 36 possible rolls.

Now that we've found the number of possible outcomes, we need to find the number of <em>desired</em> outcomes. What are our desired outcomes in this problem? They are asking for all outcomes where there is <em>at least one 5 rolled</em>. It turns out, there are only 3:

(1) D1 - 5, D2 - Anything else, (2), D1 - Anything else, D2 - 5, and (3) D1 - 5, D2 - 5

So, we have \frac{3}{36} = \frac{1}{12} probability of rolling at least one 5.
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