Question
4.) you have 10 $1 chips to play. think of 10 numbers between 00, 0, 1 and 36, and then use a random number generator to create a list 10 random numbers between 00, 0, 1 and 36 (how will you distinguish between 0 and 00?). the randomly chosen numbers represent 10 consecutive spins of the roulette wheel. assuming that you played your chosen numbers (straight) in the same consecutive games (in the order listed), how many times did you win? is this what you expected?
59%. 1 :24 PM Roulette.pdf Let's caenlate the odds o hets played in the gae onette. In the Amcrican version of the pame, players may choosc to ple brts on cither a single mmber or a Tan ofmbers, the cnlons red or hlark, or whether the mumher is odd or ven. To drtermie the wing nmber nd color, a croupicr spins a whee in one dirctiom, then spins a hall in the uppusile diretou aud a iled circark na e cmerence ol the weel. The ball eveulually kose- iuuuleiiluu and lalls oil lu llue wleel aud inlu one u[ 38 oulured and uuullered podessou the wheel. Ist 12 2nd 12 -3rd 12 1-18 | Even | | Odd | 19-36 There are varions types of possible bets in Ronette. Iuside bets -Straight (35 to 1)-A single number betThe chip is placed entirely on the middle of a number sqnare. Split (17 to 1)-A bel ou two adjoining uumbers. either ou the vertical or horizontal (as in 14-17 or 8-9). - Street (11 to 1) A bet un three bers on a single horiontal lie. The chip is placed on the edge of the - Corner (8 to 1) -A on four numbers in a square layout (as in 11-1214-15). The chip is plaoed at the - Double Street (5 to 1)-Abet on two adjoining stroets, with the chip placod at the corresponding intersection, - Basket 11 to 1) A bet D, 1, aad2: . ad 2; or 0D, 2, and 3. The chip is placed at the intersection - Top Line to 1) A bet , 1, 2, and 3. The chip is placed either at the corer of ad 1, or the The chip is plaeed on the line betweem these numbers. line of a uber at the e of te lin either the let or the riglht, depending on the layuut). horisontal and vertical intersection of the lines between the four nbers as if in between where two stroet bets wod be plaood of the three desirod numbers coruer of OD ad 3. Outside bets - 1 to 18 (1 to 1)- A bet theow eighteen mbers nou-zero). - 19 to 36 (1 to 1) A beton one of the latter bigh eighteen numbers, - Red or Black (1 to 1)- A bet on color nogreen). -Even or Odd1 to 1)- A bet oa an even or odd nozero number -Dozen Bets (2 to 1)-A bet on the first (1-12), second (13-24), or third group (25-36) of twelve numbers. - Column Bets (2 to 1)- A ben 12 numbers on any of the three vertical lines (such as 1-4-7-10 on down to 34), The chip is placed on the space below the final number in this string
Explanation / Answer
4)
I have chosen the below 10 numbers for each 10 consecutive spins of the roulette wheel.
21, 14, 14, 31, 14, 13, 00, 9, 34, 9
I have randomly generated numbers representing 10 consecutive spins of the roulette wheel. (Using R)
7, 10, 27, 36, 10, 5, 14, 19, 13, 30
None of the times my chosen number matches with the spins of the roulette wheel. So,I have won 0 times.
The expectation of binomial distribution with n spins and probability of winning is n*p.
The total number of numbers = 38
So, the probability of winning of randomly chosen number = 1/38
n = 10
So, the expected number of wins in 10 rollete spins = 10 * (1/38) = 0.2632
So, you will win 0.26 times on average in 10 spins.
