Final answer:
To find the probability of rolling an even number exactly two times when a six-sided die is rolled six times, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Step-by-step explanation:
To find the probability of rolling an even number exactly two times when a six-sided die is rolled six times, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
Step 1: Find the number of favorable outcomes - In this case, there are three ways to have exactly two even numbers: (EEEOOO, EOEEOO, or EOOEEO), where E represents an even number and O represents an odd number.
Step 2: Find the total number of possible outcomes - Each roll of the die has 6 possible outcomes, so when rolled six times, there are a total of 6^6 = 46656 possible outcomes.
Step 3: Calculate the probability - The probability is equal to the number of favorable outcomes divided by the total number of possible outcomes. Therefore, the probability of rolling an even number exactly two times is 3/46656 or approximately 0.0000643.