if you roll two fair six - sided dice, what is the probability that at least one die shows a 3?
if you roll two fair six - sided dice, what is the probability that at least one die shows a 3?
Answer
Explanation:
Step1: Calculate total outcomes
When rolling two six - sided dice, the total number of outcomes is $6\times6 = 36$ since each die has 6 possible results.
Step2: Calculate the number of outcomes with no 3s
The first die has 5 non - 3 outcomes, and the second die also has 5 non - 3 outcomes. So the number of outcomes with no 3s is $5\times5=25$.
Step3: Calculate the number of outcomes with at least one 3
The number of outcomes with at least one 3 is the total number of outcomes minus the number of outcomes with no 3s. So it is $36 - 25=11$.
Step4: Calculate the probability
The probability $P$ of getting at least one 3 is the number of favorable outcomes (at least one 3) divided by the total number of outcomes. So $P=\frac{11}{36}$.
Answer:
$\frac{11}{36}$