Final answer:
The probability of the product being even when two six-sided dice are rolled is 3/4 or 0.75, since there is a 1/2 chance of rolling an even number on each die, and the only way to have an odd product is if both dice show odd numbers.
Step-by-step explanation:
To solve this problem, we will find the probability that the product of two rolls of a six-sided die is even. The product of two numbers is even if at least one of the numbers is even. In the case of a six-sided die, there are 3 even sides (2, 4, 6) and 3 odd sides (1, 3, 5).
For the first roll, the probability of rolling an even number is 3 out of 6, or 1/2. The second roll is independent of the first, so the probability of rolling an even number again is also 1/2. To find the probability that at least one roll is even, we can use the complement rule which states that the probability of an event 'E' is 1 minus the probability of the event's complement. The only way not to get an even product is to roll two odd numbers.
The probability of rolling an odd number on the first toss is 3/6, and similarly 3/6 for the second toss. Therefore, the probability of both being odd is (3/6) × (3/6) which simplifies to 1/4. Hence, the probability of at least one die being even (and therefore the product being even) is 1 - 1/4 = 3/4.
The final answer is that the probability of getting an even product from two rolls of a six-sided die is 3/4 or 0.75.