No, Thomas Crapper did not invent the flush toilet and thus give his name to posterity. The word crap, meaning excrement, is from the Old French, via Middle English, crappe, which stood for the grain that was trodden underfoot in a barn. The word originally derives from the Latin crappa.
But there was a Thomas Crapper, and he did improve, but not invent the flush toilet. He was an Englishman, 1837-1910, who invented the ball and suction device (British Patent # 4,990) found in modern toilets that allows an efficient flush with an minimum of water and also shuts off the flow to the tank once refilled. This was a case where an appropriately named man made a contribution, not a case of an eponym. The OED2 traces its use at least to 1846, crapping ken for a water closet. Since Crapper did not invent his version of the toilet until 1882, it is obviously not the origin.
Incidentally, the word craps, for the dice game, derives from the word crab and is unrelated to the term for excrement. It is a French corruption of the English term which stood for a throw of two or three. Why the English called such a toss crabs is not known, but according to the OED2, it dates at least to 1768. The tale that it derives from the nickname of Bernard de Marigny, a New Orleans gambler (circa 1800) known as Johnny Crapaud, literally Johnny Toad, is fanciful, but not the correct etymology.
POWERBALL LOTTERY MATH PROBABILITY
The most popular method used by players for the selection of lottery numbers is calendar dates such as birthdays or anniversaries.
More than 65% of the tickets played in state lotteries have numbers all marked under 31. By eliminating numbers above 31, two problems emerge.
First, there is a much greater chance of sharing the bootie because such a high percentage of people, like yourself, play this way. It is odd, Dale, to have only one winner when all the numbers picked are under 31.
Second, track your state lottery draws and note how often just the numbers 1-31 occur. Fortunately for you, I did the homework by researching every draw of every Togel Singapore game ever played in California. Even to my surprise, a ticket limiting the numbers between 1-31 appears, on average, only 3.5 times a year (104 games per year-Wednesday and Saturday draws).
So for the above two reasons, Dale, I subjectively recommend random numbers, in addition to waiting for the lottery to get close to true odds.
For your second question, I list the staggering chance of hitting the Illinois lottery (6 out of 54) below, plus additional state lottery games, indexed in ascending order of difficulty.
6 out of 25 1 chance in 177,100
6 out of 30 1 chance in 593,775
6 out of 33 1 chance in 1,107,568
6 out of 36 1 chance in 1,947,792
6 out of 39 1 chance in 3,262,623
6 out of 40 1 chance in 3,838,380
6 out of 41 1 chance in 4,496,388
6 out of 42 1 chance in 5,245,786
6 out of 44 1 chance in 7,059,052
6 out of 46 1 chance in 9,366,819
6 out of 47 1 chance in 10,737,573
6 out of 48 1 chance in 12,271,512
6 out of 49 1 chance in 13,983,816
6 out of 50 1 chance in 15, 890,700
6 out of 51 1 chance in 18, 009,460
6 out of 54 1 chance in 25,827,165
Powerball (5 out of 45 + 1 out of 45) 1 chance in 55 million.