If two six-sided dice are rolled, the probability that they both show the same number can be expressed as ab where a and b are coprime positive integers. What is the value of a+b?
prob(both have the same) = 6/36 = 1/6
you do the a and b stuff
To find the probability that two six-sided dice show the same number, we need to count the number of favorable outcomes (i.e., both dice showing the same number) and the total number of possible outcomes.
Step 1: Counting the favorable outcomes:
There are six possible outcomes for each die, as there are six sides labeled with numbers 1 through 6. For the two dice to show the same number, we have six possible pairs: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6). So, there are 6 favorable outcomes.
Step 2: Counting the total number of outcomes:
Since each die has 6 possible outcomes, the total number of outcomes for rolling two dice is 6 * 6 = 36.
Step 3: Calculating the probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of Favorable Outcomes / Total Number of Outcomes
= 6 / 36
= 1/6
Therefore, the probability that two six-sided dice show the same number is 1/6.
To express the probability as ab, where a and b are co-prime positive integers, we see that a = 1 and b = 6.
Therefore, a + b = 1 + 6 = 7.