Yeah, yeah, that famous ‘bias’ — especially the one when the opponent refuses to ignore the obvious facts that are… uncomfortable for your particular agenda. 
What’s there to calculate? If your starting hand is 3 cards and you ‘mulligan’ it all, then by turn 4 you’d have drawn 10 cards out of 30 in your deck (naturally, without any additional draw, but you can account for that Chillfallen Baron separately if you want to, it’s not hard — see below), so that’s a conditional probability of 1/3 to get that one card. There’s also a 3/30 chance to get it in the opening hand, so the total chance is about 0.9*1/3 + 0.1 = 0.4 (ignoring the intricacies of ‘mulliganning’, if HS has any — I dunno).
If you go second, then the starting hand is four cards, so you have 4/30 + (26/30) * (2*4+4)/30 = 0.48 (I actually bothered to use a calculator for it, lol).
If you assume that chances to go first and second are equal (which, by the way, is just an assumption, a theory — just because they’re strictly equal for all players combined, obviosuly, doesn’t mean you’re not gonna get advantaged or disadvantaged), then the total average chance is 0.5 * 0.4 + 0.5 * 0.48 (otherwise you could substitute your actual probabilities as ‘weights’) = 0.44 .
You don’t need any analysis (calculus) or ‘fancy’ probability theory for these simple estimates, anyone who hasn’t skipped maths (and grammar, but that’s not the point here) classes at school in favour of playing Hearthstone 
or something like that should be able to do it, I think. However, I’m not suprised maths is not the fad on these forums — it’s mostly those guys armed with their ‘OPINIONS’… I was looking for a suitable link, found this — it’d do, I guess: Even single-player game is rigged ; that topic is surprisingly (or not, given how repetitive these forums are) relevant, even that old nonsense about ‘bias’ was mentioned yet another time there.
Ever had one of those moments when you for once said something meaningful without even realising it? You probably had it then, but didn’t realise it.
(Upd.: typo fixed)