To determine the probability that both dice show an odd number, we first need to identify the odd numbers on a six-sided die. The odd numbers are 1, 3, and 5. This means there are a total of 3 odd numbers out of 6 possible outcomes for each die.
Now, the probability of rolling an odd number on one die is:
P(odd) = Number of odd outcomes / Total outcomes
Which translates to:
P(odd) = 3 / 6 = 1 / 2
Since the rolls of the two dice are independent, we multiply the probabilities of each die showing an odd number:
P(both odd) = P(odd on first die) * P(odd on second die)
Thus, we have:
P(both odd) = (1/2) * (1/2) = 1/4
This means the probability that both dice show an odd number is 1/4 or 25%.