Comparing Proportions with difference numbers of events

So, I'm interested in examining prey preference of a predator and one of the metrics I am interested in rejection rates for attack. I have 1 hour trials where a predator is offered two different prey items and I count the number of times each prey item is rejected. I am interested in comparing rejection rates between the two prey, but the rejection rates can be heavily skewed based on the number of each prey item encountered.

For example in trial #1 Prey #1 may be rejected 50% of the time with only two enounters (1/2), while prey #2 may be rejected 50% of the time with 20 encounters (10/20). The rejection rates are the same but calculated from very different number of events. So my question is, is there some way to take into account 50% rejection based on 2 encounters vs. 20 encounters? I was considering running a paired t-test on the rejection rates, but the difference in events concerns me.

Thank you!