To determine the probability that both dice rolls result in odd numbers, we need to follow these steps:
1. Identify the possible outcomes for one dice roll. A standard six-sided die has six faces numbered from 1 to 6. The odd numbers on the die are 1, 3, and 5.
2. Determine the probability of rolling an odd number on one die. There are three odd faces out of the six possible faces, so the probability of rolling one odd number on a single die is 3 out of 6. This simplifies to 1/2 because 3/6 is equivalent to 1/2 after dividing both the numerator and the denominator by 3.
3. Since the dice rolls are independent events (the result of one roll does not affect the result of the other), we multiply the probabilities of each individual dice roll to obtain the joint probability of both events occurring.
4. Calculate the joint probability of rolling an odd number on both dice. The probability on one die is 1/2, and for two dice, it's (1/2)*(1/2), which equals 1/4.
Therefore, the probability that both dice rolls result in odd numbers is 1/4, making the correct answer:
1/4
