Hi Ron,
I'm sure it didn't escape you that I said "merely very unlucky" was the best answer, not in an absolute sense, but in comparison to the other five choices.
Actually, you didn’t say that, but I understood that was part of your reasoning.
All you did was criticize my reasoning
Wow! You are touchy!
Your reasoning was worthy of criticism, but what I did was give an opinion, supported with math-based comparisons to probabilities of familiar games of chance. The math comparisons articulate the ratios or the equivalent number of sequential statistical successes for unlikely and extremely unlikely events. While these articulations contradict your reasons for selecting “merely very unlucky,” they do not overtly criticize your reasoning. I’m sure you’ve read enough of my posts to know when I’m criticizing. (I’m still LMAO over the Gracie Allen comment. –It’s my best one-liner troll post ever.)
...Continuing with the postscript assessment:
My introduction to the post,
“Merely Unlucky? No! Not merely. This unlucky series of failures is astronomically unlikely,”
is my articulation of disagreement for the use of the word “merely,” which was intentionally used by the teacher who wrote this question to trivialize or down play the “very unlucky” part of the phrase. The word “simply” could be substituted for “merely” as it is used in this context.
Simple things happen frequently, complex things happen less frequently. But there is nothing simple about a series of events, that when aggregated, is so statistically unlikely that before it happens the Earth’s sun will be a cold brown dwarf (if it still exists at all), the Milky Way galaxy will with merge with the Andromeda galaxy, a team from the PeeWee football league will win the Super Bowl, and CPhill will have extracted the Roman Zero from Sisyphus’s Bolder.
The "e." answer does include the word "very" which, as you've demonstrated – I'm assuming your calculations are accurate, or at least, accurate enough – is an apropos modifier. Maybe it should have been in an emphasized typeface, but I'm not the one who posted the question.
There are probably no words typically used as modifiers in English, Latin, Greek, or any language that can conveniently depict the absurd statistical improbability of this hypothetical question, – at least, not without sounding hysterical.
Here’s an analogy:
To bottle all the water in the Atlantic Ocean requires a very large number of gallon jugs. As you may see, though true, it’s an understatement. It’s absurd.
To bottle all the water in the Atlantic Ocean merely requires a very large number of gallon jugs. Adding ‘merely’ makes it absurdly funny.
The modifiers in this answer are intentionally used to teach novice students about highly improbable events.
...I'm assuming your calculations are accurate, or at least, accurate enough...
They are, but for most novice students of statistics, the path will be a long one before they begin to understand the significance. While many can at least intuit an understanding for large ratios, the enormity of the numbers in the ratios is lost to them. It’s worse with the sequential successes of highly improbable events. For example they see the royal flush and think “Oh, I only need three (3) of these in a row. Three is a low number –that shouldn’t be too difficult to do.”
Most students will not realize that a professional poker player will likely never have a natural royal flush in a five-card poker game, and will only see two, in their entire careers. And in a billion billion life times they will never see two in a row, let alone three.
...and I did get a Royal Flush. No joker, no wild cards at all, just the 10 thru Ace of hearts, and I didn't draw to it, I received it on the deal.
Congratulations. It’s too bad you only won macaroni!
Were you playing five-card or seven-card poker? It’s (1/649740) for five-card and (1/30940) for seven-card poker. The seven-card is (21) times more likely, but still amazing. In my logbook where I’ve recorded over 29,000 poker games, I’ve never had a natural royal flush. I’ve had a natural king-high straight flush twice, and one queen high straight flush. It’s worth noting that in seven-card poker the royal flush is slightly more likely to occur than the other straight flush hands. In five-card poker, the probability is the same for any given high-card.
So, unlikely is not synonymous with impossible.
You’re right, it’s not.
What infinitesimal number is small enough to be synonymous with zero?
How small does a probability have to be before it becomes synonymous with impossible?
How about this one?
What’s the probability that a single shuffle of a randomized standard deck of 52 cards returns to its factory-sealed box order of A-K spades, A-K hearts, A-K clubs, and A-K diamonds?
Shuffling the cards once per second, how long would it take before the expectation of (1) success reaches a probability of (63.21%)? At this point in time, how many statistical successes will our coin-flipping-roulette player have?
I'll answer the last question.
\(\large \log_{576460752303423488}(52!) \approx 3.82 \) statistical successes
So if our coin-flipping-roulette player takes forever to have one success, then our shuffler will take (3.82) forevers.
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you neglected to say which choice you think would be better, perhaps that wasn't an oversight.
You are right, it wasn’t an oversight: My offer “...to bet a Rouble that that some Russian fucked with the Roulette wheel,” implies answer (b).
I’m still willing to make the wager. A Russian Rouble is 0.014USD; that’s about 8 elbow macaroni noodles. You know, my point in making the wager was to encourage you to use your noodle –to think outside of the box (of macaroni). 
GA
+2489 
