Two dice are rolled. Find the probability of the following event. The first die is 5 or the sum is 6.

  5/18

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Explanation:

A = number of times we get 5 on the first die

B = number of times we get a sum of 6.

Refer to the sum of dice chart below. This chart represents every possible sum of two dice (eg: 1+1 = 2 in the top left corner or 6+6 = 12 in the bottom right corner).

Let's say the blue die is the first of the pair.

Locate 5 on the blue die and notice there are 6 occurrences when this happens. This corresponds to the 6 other possibilities for the red die. So we have A = 6.

Also notice how there are 5 occurrences of the sum "6" in the table. So B = 5.

We have A+B = 6+5 = 11 occurrences of either the first die is 5 or the sum is 6. However, we have to subtract off 1 because we double counted "6" when adding A and B.

So in reality we have 11-1 = 10 times this happens.

This is out of 36 total ways to roll two dice.

Therefore, the probability we want is 10/36 = 5/18

true

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