What methods can I research to help me estimate a probability This is my first question on here, I hope it goes well... I need to estimate the probability of an event that I don't have historical data on, but I do have data on similar/comparable events. I hope this is not too general. For example, take the damage rate of one item with one particular; this is a simple count, did the item get damaged--Yes/No and convert to a rate. I believe this data is characterized by a binomial distribution. Is there a method that I can apply to estimate the damage rate of another similar item based off the item I do have data on??

Suppose items come in boxes of $n = 24,$ then the number $X$ of defective items in a box might be modeled as $\mathsf{Binom}(n=24, p = .01)$ so that you'd expect an average defective rate of $\mu = np = 0.24$ per box.
Then if you got $y = 6$ defects in ten boxes, you might wonder
if you got a shipment of boxes with higher than the usual defective rate. It would be fair to text the the null hypothesis $H_0: p = 0.01$ against $H_a: p > 0.01$ based on $y = 6$
defects in $n = 240.$
In R, an exact binomial test would look like this:
binom.test(6, 240, p=0.01, alt="g")

        Exact binomial test

data:  6 and 240
number of successes = 6, number of trials = 240, 
 p-value = 0.03489
alternative hypothesis: 
 true probability of success is greater than 0.01
95 percent confidence interval:
 0.01094225 1.00000000
sample estimates:
 probability of success 
                  0.025 

The P-value $0.03489 < 0.05 = 5\%$ indicates significance
at the 5% level. Also, the lower bound on the one-sided confidence interval for $p$ is $0.011 > 0.01,$ also suggesting
incompatibility of six defects in 240 items as inconsistent
with a 1% defect rate.
Notes: (1) A direct computation of the (one-sided) P-value in R
is shown below.  $P(X \ge 6; n=240, p=0.01)$ $=
1 - P(X \le 5; n=240, p=0.01)$ $= 0.03488787.$
1 - pbinom(5, 240, .01)
[1] 0.03488787

(2) If you're dealing with thousands of items,
you might want to use a Poisson model.
For values of interest here, the distributions $\mathsf{Binom}(240, 0.01)$ and $\mathsf{Pois}(2.4)$
are very nearly the same.

R code for figure:
x = 0:10
pdf.b=dbinom(x, 240, .01)
pdf.p=dpois(x, 2.4)
hdr = "Distributions of BINOM(240, 0.01) [bars] and POIS(2.4) [dots]"
plot(x, pdf.b, type="h", lwd=3, col-"blue", main=hdr)
 points(x, pdf.p, pch=19, col="orange")
  abline(h = 0, col="green2")
  abline(v = 0, col="green2")

