We know that the probability is 0.5 for 5 heads out of 10 tosses and likewise, 0.5 for 50 heads out of 100 tosses. However, we will say the probability of 0.5 from 100 coin tosses is preferable because we have tried more coin tosses but I don't know how to support my opinion.

Some says Hoeffding's Inequality but I am not sure that is going to help support my opinion since Hoeffding's Inequality looks like I could use that inequality for the number of data when I expect how small the error should be.[I am not sure if I am correct. I am still trying to understand the inequality. I am just saying it with how much I know, so far.]

Is there any theory to support that the probability of 0.5 from 100 tosses is better than the probability of 0.5 from 5 heads out of 10 tosses?