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: 6×6=366 \times 6 = 36

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: 3×3=93 \times 3 = 9

Step 3: Calculate the probability.

The probability is the ratio of the number of favorable outcomes to the total number of outcomes: Probability=Number of favorable outcomesTotal number of outcomes=936=14\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{9}{36} = \frac{1}{4}

Final Answer:

The probability that both dice show even numbers is 14\frac{1}{4}.


Would you like to know more details or have any other questions? Here are some related questions you might find interesting:

  1. What is the probability that at least one die shows an even number?
  2. What is the probability that the sum of the numbers on the two dice is even?
  3. If you roll three dice, what is the probability that all three show even numbers?
  4. What is the probability that the product of the numbers on the two dice is even?
  5. 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.

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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

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Suitable Grade Level

Grades 6-8