A die is tossed thrice. Find the probability of getting an odd number at least once.

Explanation

To find the probability of getting an odd number at least once when a die is tossed thrice, we can follow these steps:

### Step 1: Understand the total outcomes
When a die is tossed, there are 6 possible outcomes: {1, 2, 3, 4, 5, 6}. Among these, the odd numbers are {1, 3, 5} and the even numbers are {2, 4, 6}.

### Step 2: Calculate the probability of getting an even number
The total number of even numbers on a die is 3 (2, 4, 6). Therefore, the probability of getting an even number in a single toss is:
\[ P(\text{Even}) = \frac{\text{Number of even outcomes}}{\text{Total outcomes}} = \frac{3}{6} = \frac{1}{2} \]

### Step 3: Calculate the probability of getting even numbers in all three tosses
Since the tosses are independent, the probability of getting an even number in all three tosses is:
\[ P(\text{Even in all three tosses}) = P(\text{Even}) \times P(\text{Even}) \times P(\text{Even}) = \left(\frac{1}{2}\right)^3 = \frac{1}{8} \]

### Step 4: Calculate the probability of getting an odd number at least once
To find the probability of getting an odd number at least once, we can use the complement rule:
\[ P(\text{Odd at least once}) = 1 - P(\text{Even in all three tosses}) = 1 - \frac{1}{8} \]
Calculating this gives:
\[ P(\text{Odd at least once}) = 1 - \frac{1}{8} = \frac{8}{8} - \frac{1}{8} = \frac{7}{8} \]

### Final Answer
Thus, the probability of getting an odd number at least once when a die is tossed thrice is:
\[ \frac{7}{8} \]

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