• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

THE DICE GAME - calculating probabilities

Extracts from this document...



In the real world events can not be predicted with total certainty. The best we can do is say how likely they are to happen, using the idea of probability.

Probability of an event happening =

Number of ways it can happen


Total number of outcomes

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common usage, the word "probability" is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%. The analysis of events governed by probability is called statistics.

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments.

SHORT EXPLANATION: Each *point* is considered as a separate task.

...read more.


Ann-2, Bob-3

Ann-3, Bob-3

Ann-4, Bob-3

Ann-5, Bob-3

Ann-6, Bob-3

Ann-1, Bob-4

Ann-2, Bob-4

Ann-3, Bob-4

Ann-4, Bob-4

Ann-5, Bob-4

Ann-6, Bob-4

Ann-1, Bob-5

Ann-2, Bob-5

Ann-3, Bob-5

Ann-4, Bob-5

Ann-5, Bob-5

Ann-6, Bob-5

Ann-1, Bob-6

Ann-2, Bob-6

Ann-3, Bob-6

Ann-4, Bob-6

Ann-5, Bob-6

Ann-6, Bob-6

(The bold combinations are cases in which Ann wins.)


A = case where Ann is winning

B = case where Bob is winning

N = case neither Ann and Bob is winning

Since both have dices with 6 sides, the total number of combinations when both rooling is 6 x 6 = 36.

The dice will match 6/36 of the time. Means in 6/36 of the time both will have equal number on the dice.

Each player will have the higher number in 15/36 of the time.




With ties going to Bob, Ann wins 15/36 or total of 41.6666...67% => ~41.7%.






1-(21/36)^2 is the chance for Ann to win if, when she loses the first time, both of them roll again.

...read more.


A = case where player is winning. P(A) = 15/36

B = case where bank is winning. P(B) = 21/36

P is pay out, the amount of the bank pays if the player win.

V is betting value, the amount of money the player has to pay each time she/he wants to play.

Now, lets calculate for a fair game

E = P(A) * P - P(B) * V

0 = 15/36 * P - 21/36 * V

so we have the ratio P = 21/15 * V

In case they roll to infinity and the player finally win the game

Winning - 1st roll = 15/36

Winning - 2nd roll = 21/36 * 15/36

Winning - 3rd roll = 21/36 * 21/36 * 15/36

Sum of all (with geometric progression)

S = t_1 / (1-r)

S = (15/36) / (1-21/36)

S = 15/15

This cannot be right because the calculated probability is 1.

Bank wins the game

Winning - 1st roll = 21/36

Winning - 2nd roll = 15/36 * 21/36

Winning - 3rd roll = 15/36 * 15/36 * 21/36

Sum of all (with geometric progression)

S = t_1 / (1-r)

S = (21/36) / (1-15/36)

S = 21/21

This cannot be right because the calculated probability is 1.

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Maths essays

  1. Math Studies I.A

    $4,500 (2007 est.) $4,000 (2006 est.) note: data are in 2008 US dollars Germany $34,800 (2008 est.) $34,900 (2007 est.) $34,000 (2006 est.) note: data are in 2008 US dollars Ghana $1,500 (2008 est.) $1,400 (2007 est.) $1,300 (2006 est.)

  2. Math Studies - IA

    Hence the two variables are independent. No association exists. As a final step, to resolve some of the contradictions in the data, the basis of all mathematics, logic, was used.

  1. Math IA type 2. In this task I will be investigating Probabilities and investigating ...

    The possible limitations to this value might be that although, Ben and Adam know that Adam wins twice as many points as Ben does, still conditions in practice may vary and a change in these conditions such as weather change, injury, illness etc.

  2. Modelling Probabilities in Tennis. In this investigation I shall examine the possibilities for ...

    For instance, the arrangement 'AAAABBB' would finish at 4 points, with the score 4-0. We can therefore subtract such instances to work out the number of games of exactly y points. y=4: y=5: y=6: y=7: Note that each of these numbers represents the number of games of exactly y points, with either A or B winning.

  1. Stellar Numbers. In this task geometric shapes which lead to special numbers ...

    I.e.: 6Sn = 6Sn-1 + 12n To prove my equation I will use an existing example from above and then prove it with one stage further. For Stage 3: 6Sn = 6Sn-1 + 12n 6S4= 6S3 + (12x3) = 37 + 36 =73 For stage 8: 6Sn = 6Sn-1 + 12n 6S8 = 6S7 + (12x7)

  2. This essay will examine theoretical and experimental probability in relation to the Korean card ...

    I will start by giving brief idea on what is probability and how it relates to the real life world situations. I will then start examining the chances of getting each hand with "Sut-Da" then compare with the experimental value.

  1. The purpose of this investigation is to create and model a dice-based casino game ...

    and (b,a). Therefore, the number of outcomes where player A rolls the higher number is equal to the number of outcomes in which player B rolls the higher number, or one-half of all the outcomes in which both players roll different numbers.

  2. Modelling Probabilities on games of tennis

    = nCxpx qn-x 1. The probability of Adam winning ?X? number of points can be found by substituting ?X? with the number of points that Adam wins and after solving, the answer will be Adams probability of winning the given number of points that were substituted into the equation.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work