Crossing tomato plants should give birth to a new population of plants of 4 types that we'll call $P_1$, $P_2$, $P_3$ and $P_4$. According to theory, the ratios of appearance of these 4 should be $\frac{9}{16}+t$, $\frac{3}{16}-t$, $\frac{3}{16}-t$ and $\frac{1}{16}+t$ respectively.
Now some scientists perform $1611$ tests and get the following results : $P_1$ $926$, $P_2$ $288$, $P_3$ $293$ and $P_4$ $104$.
I'm trying to write down the likelihood of $t$ given these observations. I think I'm getting this wrong! I've used the formula $P(A \cap B \cap C \cap D)=P(A)P(B|A)P(C|A \cap B)P(D|A \cap B\cap C)$ where here I use $A$ the event that the number of plants of type $P_1$ is $926$, ...
So I have $P(A) = \frac{1611!}{926!(1611-926)!}(\frac{9}{16}+t)^{926}(1-\frac{9}{16}-t)^{1611-926}$, and for the other factors, I change the elements $1611$, $926$ and $\frac{9}{16}+t$ appropriately...
It gives a really complicated result, do I have the idea? I doubt it...