If two six-sided dice are rolled, the probability that they both show the same number can be expressed as a b where a and b are coprime positive integers. What is the value of a+b ?
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What is a and what is b?
To find the probability that two six-sided dice show the same number, we first need to determine the total number of possible outcomes when rolling two dice. Each die has six sides, so there are 6 possible outcomes for each die. Since we are rolling two dice, the total number of outcomes is found by multiplying the number of outcomes on each die: 6 * 6 = 36.
Now, let's determine the number of favorable outcomes, which is when both dice show the same number. There are 6 ways for both dice to show a 1, 6 ways for both dice to show a 2, and so on, until 6 ways for both dice to show a 6. Therefore, there are 6 + 6 + 6 + 6 + 6 + 6 = 36 favorable outcomes.
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes. In this case, the probability of both dice showing the same number is 36/36 = 1.
Since 1/1 is already in the form of coprime positive integers, the value of a is 1 and the value of b is 1. Therefore, the value of a + b is 1 + 1 = 2.