probability - Same number multiple times on a dice roll

I was playing a game last night that involved rolling ONE die/dice. Within about 10 rolls, the person I was playing with and I rolled a 5 or a 6 at least 50% of the time. It got me thinking.

I'm interested in knowing:

1. What is the probability of rolling any 2 numbers 50% of the time within 10 dice rolls (each time rolling one die/dice)?




2. What is the probability of rolling a specific number (e.g. 5) 50% of the time within 10 dice rolls? (each time rolling one die/dice)

Looking forward to your answers. Thank you