Introduction

Being one of a

respondents or participants of monty hall game is useless if we are not

maximize the opportunity we have to obtain the best possible result of the

game. Game theory like Monty Hall oftenly isn’t being exploited well by the

participants due to their ignorance of the mathematical probability inside the

game. It is considered bias to choose whatever their intuition says instead of

calculating the probability of winning it.

In my 2 years

of IB Mathematics Higher Level, Probability is one of the core topics that I

learnt in Math HL class. This topics taught me to be more effective and

choosing the right choice in decision making to produce the best result of our

probability. In probability I often do some trials in some cases with a chance

of success but that doesn’t completely absolute.

Mathematical

Probability is a model or tools of predicting or calculating the chances that

people can exploit in order to achieve those goals of the chances they have. In

this essay, I am going to write an analysis and calculation by doing experiment

whether switching choices in the game might affect their percentage of winning.

This game basically demand us to pick 1 out of 3 choices of any variable (for

example door) that is used, 2 doors are empty or no expected gift and prize

inside it or we can say it’s a zonk while the other one contain luxurious

prizes we could not ask for any better. In this essay I’m going to explain too

about the use of conditional probability in Monty Hall game.

Background Theory

Conditional Probability

According to

Math IB Cambridge HL Textbook, “Estimate the probability that a randomly chosen

person is a dollar millionaire. Would your estimate change if you were told

that they live in a mansion?

When we get

additional information, probabilities change.

In the above

example, P(millionaire) is very different to P(millionaire|lives in a mansion).

The second is a conditional probability, and we used it in Section 22 C when

looking at tree diagrams.

One important

method for finding conditional probabilities is called restricting the sample

space. We write out a list of all the equally likely possibilities before we

are given any information, and then cross out any possibilities the information

rules out.”

So to simplify

this understanding is that just assume that a probability of event A is

calculated given that another event related has already occured, can be called

B

Fundamental formula:

Rearrangged formula of conditional probability:

Figure 1.1

shows tree diagram of conditional probability

Here above we can see that this probability

have another events that occured which form a new equation or variable ? , probability of B given that A the previous events may

affect the next events which if we calculate it (to find the prob) produce an

equation . And if we rearrange it, it becomes like the one I mentioned

above.

Data

Participants

Ace card at door

player chooses door

experimenter open door

stay

switch

1

1

2

3

lose

win

2

1

2

3

lose

win

3

1

3

2

lose

win

4

3

3

2

win

lose

5

3

2

1

lose

win

7

2

1

3

lose

win

8

3

3

1

win

lose

9

1

2

3

lose

win

10

2

2

2

win

lose

11

2

3

1

lose

win

12

3

1

2

lose

win

13

1

2

3

lose

win

14

1

2

3

lose

win

15

1

3

2

lose

win

16

1

1

3

win

lose

17

3

2

1

lose

win

18

2

2

3

win

lose

19

2

3

1

lose

win

20

2

1

3

lose

win

21

3

2

1

lose

win

22

2

1

3

lose

win

23

3

1

2

lose

win

24

1

2

3

lose

win

25

3

2

1

lose

win

26

2

1

3

lose

win

27

3

2

1

lose

win

28

3

3

2

win

lose

29

1

2

3

lose

win

30

1

1

2

win

lose

31

2

3

1

lose

win

32

3

3

1

win

lose

33

1

1

2

lose

win

34

1

2

3

lose

win

35

2

3

1

lose

win

36

3

3

2

win

lose

37

3

2

1

lose

win

38

2

1

3

lose

win

39

3

1

2

lose

win

40

3

2

1

lose

win

41

1

3

2

lose

win

42

3

1

2

lose

win

43

1

2

3

lose

win

44

2

1

3

lose

win

45

1

1

2

win

lose

46

1

2

3

lose

win

47

3

2

1

lose

win

48

3

3

1

win

lose

49

2

3

1

lose

win

50

2

1

3

lose

win