Question about the usage of Binomial dist

Hi everyone,

I have the following dillema:

Suppose you have a person A who achieved 65 successes out of 161 trials
and another person, B, who has achieved 14 successes out of 32 trials.
Which achievement is more valuable, that is, which one is less likely
to occur?

Of course, one can look at the averages but the average doesn't take
into account the consistency and the number of trials into account. (A
person who wins 500 out of 1000 times has the same average as one who
wins 1 time out of 2).

I decided to use the Binomial distribution with the MLE for each
person. That is,

Person A: p = 65/161
Person B: p = 14/32

Calculating Pr1(K=65) and Pr2(K=14) I got Pr1 < Pr2 so the first
person's achievement is more valuable.

However, I am not sure as to whether my inference is correct because
the more trials the person has, the more likely they will win.

.

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