SOLUTION: What are the odds of getting two 5's in a single throw of a pair of dice?

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Question 720886: What are the odds of getting two 5's in a single throw of a pair of dice?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
One way to solve this is:
  • There are 6 faces on a die and each face has a different number on it. So the probability of rolling a single die and getting one of those six numbers, like a 5, is 1/6.
  • When you roll two dice, the number you get on one dice in no way influences or changes the number you get on the other dice, the numbers you get are independent events.
  • The probability of two independent events is the product of the probabilities of the two individual events. So the probability of rolling two 5's is the product of probability of rolling one 5 times the probability of rolling one 5:
    %281%2F6%29%2A%281%2F6%29+=+1%2F36
Another way to figure this out is to list all the possible rolls of two dice. Make sure you count every possible roll. This might be easiest if you list them in a table like the one I'll start for you:
       1       2      3       4       5       6
  1   1+1     1+2    1+3     1+4     1+5     1+6
  2   2+1     2+2    2+3     2+4     2+5     2+6
  3
  4
  5
  6
Note how the first number of each pair in the table is the row number and the second number is the column number. If you complete this table you will find a) that there is just one 5+5; and b) there are 36 total spins of two dice. This makes the probability 1/36.