2.) suppose that my favorite number is 3 and I insist on betting on 3 in every g

Question

2.) suppose that my favorite number is 3 and I insist on betting on 3 in every game.
A.) if I play 5 games in a row, betting on 3 straight each time, what are the odds that I win at least once
B.) after playing 3 straight for several games and becoming depressed at my losses, I decide to try to win my money back. Since I also like the color red,I decide to place bets on both 3 straight and the color red. determine (by counting ) the odds that at least one of my bets wins in any given game. can the odds be calculated by using the formula, P (3,red)=P (3)+P (red)? explain
C.) the payout for a straight bet is 35 to 1 and the payout for a color bet is 1 to 1. why would someone make the bet described in (B.)? does it make more sense to be on both red and 2 straight (assuming that I can bring myself to bet straight on any number besides 3, of course)?

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

2. In a roulette game there are 38 possible outcomes. If we decide to bet on a single number say '3' then the probability of winning in any single game is 1/38. If we decide to bet on a single colour either red or black then the probability of winning is 18/38

(A) It is given that five games were played in a row, betting straight on 3 each time.

Let X denote the number of wins in the 5 plays.

Then the probability of winning atleast once is given by P(X1) =1 - P(X=0).

Now, P(X=0)=P(Zero win in 5 plays) = 37/38 x 37/38 x 37/38 x 37/38 x 37/38 = 0.8752

So, P(X1) =1 - P(X=0)
P(X1) =1 - 0.8752
P(X1) =0.1248

(B) There are 18 cells cells which are coloured red. Additionally, the cell which is numbered 3 is also coloured red. So, here both the events intersect and the total number of favourable outcomes is 18.

So, probability of winning when a bet is placed on 3 straight and the colour red is 18/38

Since, the two events coincide as the cell 3 is also red in colour.

So, in other words P(Atleast one of the bets wins) = P(Either the number 3 comes or the colour red comes)

Since the event getting 3 is a subset of getting the colour red, we have

P(Atleast one of the bets wins) = P(The colour red comes)=18/38

P(Atleast one of the bets wins) = 0.47368

Now, it is seen that

P(red)=18/38 = 0.47368

P(3)=1/38 = 0.02632

P(3,red)= 18/38 = 0.47368

So, from the above we see that P(3,red) P(3)+P(red)

(C) Betting straight on 3 and the colour red together will increase the expected payout from the game. So, it might be considered to bet in a way as described in (B).

Yes, it will be better to bet on the colour red and the number 2 because the two events are exclusive (as the number 2 is black in colour). So, the number of favourable outcomes in this case will be 18+1=19.

And the probability of winning will be 19/38 = 0.5 which is more than before.

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