Question

A die is thrown 10 times. The probability that an odd number will come up at least once is:

• A. $\frac{11}{1024}$
• B. $\frac{1013}{1024}$
• C. $\frac{1023}{1024}$
• D. $\frac{1}{1024}$

Answer 1

The Correct Option is C

1. Understand the problem:

We need the probability that at least one odd number appears when a die is thrown 10 times.

2. Calculate the probability of the complement event:

The probability of no odd numbers (i.e., all even numbers) in 10 throws:

\[ P(\text{all even}) = \left(\frac{3}{6}\right)^{10} = \left(\frac{1}{2}\right)^{10} = \frac{1}{1024} \]

3. Compute the desired probability:

\[ P(\text{at least one odd}) = 1 - P(\text{all even}) = 1 - \frac{1}{1024} = \frac{1023}{1024} \]

4. Match the result to the options:

The probability \( \frac{1023}{1024} \) corresponds to option (C).

Correct Answer: (C) \( \frac{1023}{1024} \)

Answer 2

The probability of not getting an odd number in a single throw is: \[ P(\text{not odd}) = \frac{3}{6} = \frac{1}{2}. \] The probability of not getting an odd number in 10 throws is: \[ \left(\frac{1}{2}\right)^{10} = \frac{1}{1024}. \] Thus, the probability of getting at least one odd number is: \[ 1 - \frac{1}{1024} = \frac{1023}{1024}. \]