Math Problem Statement
you roll 2 six sided dice. what is the probability that both dice show even numbers
Solution
To calculate the probability that both dice show even numbers when you roll two six-sided dice, follow these steps:
Step 1: Determine the total number of outcomes.
Each die has 6 faces, so the total number of outcomes when rolling two dice is:
Step 2: Determine the number of favorable outcomes.
The even numbers on a six-sided die are 2, 4, and 6. There are 3 even numbers on each die.
For the first die to be even, there are 3 possible outcomes (2, 4, or 6). Similarly, for the second die to be even, there are also 3 possible outcomes.
Thus, the number of favorable outcomes (both dice showing even numbers) is:
Step 3: Calculate the probability.
The probability is the ratio of the number of favorable outcomes to the total number of outcomes:
Final Answer:
The probability that both dice show even numbers is .
Would you like to know more details or have any other questions? Here are some related questions you might find interesting:
- What is the probability that at least one die shows an even number?
- What is the probability that the sum of the numbers on the two dice is even?
- If you roll three dice, what is the probability that all three show even numbers?
- What is the probability that the product of the numbers on the two dice is even?
- What is the probability of rolling two dice and getting a sum of 7?
Tip: In probability, always consider both favorable outcomes and the total number of possible outcomes to find the probability of an event.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Dice Probability
Formulas
Probability formula: P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
Theorems
-
Suitable Grade Level
Grades 6-8