if you roll two fair six - sided dice, what is the probability that both dice show an odd number?
if you roll two fair six - sided dice, what is the probability that both dice show an odd number?
Answer
Explanation:
Step1: Find total outcomes
Each die has 6 possible outcomes. When rolling 2 dice, by the multiplication - principle, the total number of outcomes is $6\times6 = 36$.
Step2: Find favorable outcomes
The odd numbers on a six - sided die are 1, 3, 5. So for the first die, there are 3 odd - number outcomes, and for the second die, there are also 3 odd - number outcomes. By the multiplication principle, the number of favorable outcomes (both dice showing odd numbers) is $3\times3=9$.
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 $P = \frac{9}{36}=\frac{1}{4}$.
Answer:
$\frac{1}{4}$