Federal fund rate cut probabilities

CFA Level III Derivatives
#1

Could someone please give some guidence on how to calculate the probability of a fed fund rate cut? I don’t seem to find an example from the text, thanks.

example
If the current federal funds rate is 1.88%, and the Fed futures contract is priced at 98.33, what is the probability of a 1) 25 bps rate cut, and 2) of a 21 bps rate cut?

My thinking is that the implied FFE rate is 100-98.33=1.67%, so for

  1. 25 bps rate cut is (1.67-1.88)/ -25 =84%
  2. 21 bps rate cut is (1.67-1.88)/- 21 = 100%

But the answer was 86% probability of a 25 bp cut, i don’t know what ive done wrong.

#2

I’ve encountered similar question on CFAI Qbank, but normally question provides range of Fed Funds Rate. e.g. 1.5 to 1.75%. Then we derive the probability using the mid-point of the range as such:

(Implied rate - Mid-point of current range)/ (Mid-point of new range - Mid-point of current range)