If a 52 card deck is randomly shuffled, and I start pulling cards one by one from the top of the deck. What is the expected number of cards I have to pull before I encounter the 1st ace OR the first jack.
Edit: I know that for just the first ace, the answer is 48/5 + 1 = 10.6 (which is the same for the first jack). However I'm unsure if the answer is the same if the question becomes 1st ace or 1st jack. Instinctually I think the expected value is lower, but I don't really know how to justify that other than we now have 2 choices to look for instead of 1, bringing our expectation down.
Edit 2: Ok so i get the idea that we can just treat these as 8 cards and use the similar method. The answer in that case is 44*(1/9) + 1 = 5.89. But what happens if I'm looking for the 4th jack or the 4th ace? This is a different question from the 4th jack or ace (which is 44*(4/9) + 4 = 23.56).