if you roll two fair six - sided dice, what is the probability that the dice show the same number?
if you roll two fair six - sided dice, what is the probability that the dice show the same number?
Answer
Explanation:
Step1: Find total number of outcomes
When rolling two six - sided dice, each die has 6 possible outcomes. By the fundamental counting principle, the total number of outcomes when rolling two dice is $6\times6 = 36$.
Step2: Find number of favorable outcomes
The favorable outcomes (where the two dice show the same number) are (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). So there are 6 favorable outcomes.
Step3: Calculate probability
The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P=\frac{6}{36}=\frac{1}{6}$.
Answer:
$\frac{1}{6}$