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 will use the concept of a binomial distribution. A die is thrown 6 times, and we define getting an odd number (1, 3, or 5) as a success.

### Step-by-Step Solution:

1. **Identify the parameters**:
- The number of trials (n) = 6 (since the die is thrown 6 times).
- The probability of success (p) = Probability of getting an odd number = 3 odd numbers (1, 3, 5) out of 6 total numbers = \( \frac{3}{6} = \frac{1}{2} \).
- The probability of failure (q) = 1 - p = \( 1 - \frac{1}{2} = \frac{1}{2} \).
...