i want to choose optimal decision from following problem Imagine having been bitten by an exotic, poisonous snake. Suppose the ER physician estimates that the probability you will die is $1/3$ unless you receive effective treatment immediately. At the moment, she can offer you a choice of experimental antivenins from two competing ‘‘snake farms.’’ Antivenin $X$ has been administered to ten previous victims of the same type of snake bite and nine of them survived. Antivenin $Y$, on the other hand, has only been administered to four previous patients, but all of them survived. Unfortunately, mixing the two drugs in your body would create a toxic substance much deadlier than the venom from the snake. Under these circumstances, which antivenin would you choose, and why?
so first off all i have concluded that, for substance $X$,i would have $90$% chance to be survivded,and for $Y$ ,i would have $100$%,so maybe it should be indicator for me to choose $Y$,on the other hand,if we consider it as a combinatoric problem,then we have $p=2/3$ if we don't die when get medical treatment, and $q=1/3$ if we do,so for substance $X$,we would have $(10!/9!)*((p)^{10})*q=0.05202459$ while for substance $Y$,it would be $4!/4!*(2/3)^4*(1/3)^0=16/84=0.19047619$
so it means that i have more chance for $Y$,so does it means that i should choose $Y$?