I am in a Super Bowl prop pool with 149 other people. There are 150 total entries. I am trying to calculate the number correct I need to win the pool. If each were a 50/50 tossup, I could do this problem. However, a number of the props have differing percent chances of being correct.

So, how do I go about calculating the chance of another player getting x% correct?

I'm interested in the answer, but also the method of solving this. Thanks in advance.

Below are the odds (that I estimated) of being correct on each prop:

0.5
0.5
0.55
0.15
0.55
0.5
0.55
0.5
0.55
0.2
0.15
0.33
0.5
0.4
0.2
0.55
0.5
0.55
0.5
0.55
0.4
0.5
0.2
0.25
0.25
0.3
0.15
0.25
0.25
0.25
0.2
0.5
0.55
0.5
0.55
0.5
0.55
0.5
0.2
0.35
0.15
0.55
0.15
0.5
0.55

I ballparked the answer at 24, grouping the props by the percent chance of getting it right that I estimated, and then doing individual binomial distributions for the groups, and finally multiplying all of the resulting %age of getting X correct from each group. I assume this is pretty close.

Out of 150 people, one person should get 24+

I'd still be interested in figuring out how to do this correctly.

Thanks.

(Note: I coincidentally ended up with 24 correct, but was beat out by 5 people, including the winner, who got 27.)