i already gave you the number. and

**my professor was very clear "u dont need to use binomial distribution for that task"!**
he the author of the book:

https://digikogu.taltech.ee/et/Download/32c8edd9-f716-409a-8bce-76c189bea0cf
task 2.24, page 143.. answer given at page 664.

**0,7^12 + 0,7^13 + 0,7^14 + 0,7^15**
0.013841 +0.009689 +0.006782 +0.004748 =

**0.035**
all i needed was a verification.. one that you are clearly incapable of providing. but

**i see you point**, and i was having the same doubts about his solution. i think he maybe just wrong.

like, the probabilities are given for single votes, not the total outcome. so why doesn't he include the combinations into the sample space?

also, by his algorithm receiving at least 3 votes has a probability of 113%,

also, wouldn't 12 votes have the same probability as 12 votes, including 3 denials. cause how else would we apply the same algorithm if expected outcome would be 4 greens, 5 yellows and 6 reds.

what vexes me most, is that

**later in his book, he has a chapter about binomial distribution**,