A die is thrown 6 times. If getting an odd number is a success, what is the probability of(i) 5 successes?(ii) at least 5 successes?(iii) at most 5 successes?

Explanation

To solve the problem, we need to determine the probability of getting odd numbers when a die is thrown 6 times. We will use the binomial distribution formula for this.

### Step-by-Step Solution

1. **Identify the Probability of Success (p) and Failure (q)**:
- When rolling a die, the odd numbers are 1, 3, and 5. Therefore, the probability of getting an odd number (success) is:
\[
p = \frac{3}{6} = \frac{1}{2}
...