Final answer:
The probability of two dice showing at least one odd number is calculated by finding the total favorable outcomes (32) and dividing by the total outcomes (36), giving us a simplified probability of 8/9 or approximately 0.8889.
Step-by-step explanation:
To estimate the probability of two dice showing at least one odd number, we must first recognize there are 6 x 6 = 36 possible outcomes when rolling two dice. An odd number appears on a die if it lands on 1, 3, or 5. Therefore, the event 'at least one odd number' includes the outcomes where at least one die shows 1, 3, or 5, and, conversely, excludes the event where both dice show an even number (2, 4, 6).
There are 3 ways for an odd number to appear on one die, and since there are two dice, we square this to get 3 x 3 = 9 outcomes for both dice to show an odd number. To find the number of outcomes where at least one die shows an even number, we calculate the total outcomes (36) minus the outcomes where both dice show an even number (2 x 2 = 4 outcomes). This gives us 36 - 4 = 32 favorable outcomes (where at least one die shows an odd number).
The probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is 32/36. Simplifying this fraction, we get 8/9. So the probability of rolling at least one odd number on two dice is 8/9, or approximately 0.8889 when rounded to four decimal places.