A graduate student preparing for their child’s birthday was tes>ng toy baQeries at random. A bag of 13 AAs they had on hand had only 10 that were good. Not knowing baQery condi>ons, the student began selec>ng baQeries at random, tes>ng them one by one without replacement and then seSng tested baQeries aside in the order of tes>ng but without no>ng the results of the test. GeSng ready to test the 5th baQery, the student realized they did not remember the result of the first baQery test, only that the last three baQeries had been found good. What is the probability that the first one was good also?