A fair 6-sided die is rolled 10 times (each roll is independent). What is the probability that the rolled die will not show an even number? (That every roll is odd)

1/1024.

Step-by-step explanation:

There are 3 odd numbers in the numbers from 1 to 6. So:

Probability (one toss is odd) = 3/6 = 1/2.

So the Probability (10 tosses are all odd) = (1/2) ^10

= 1/1024.