# Ib math sl ia samples

Mar 29, 2018

Maths IA

Probability and expectation

Rationale

F

rom age of 14, I started to play cards games with my friends, it

developed an interest to win among my friends. So I thought to calculate

the relationship between card games and its probability to know my

chances of winning or losing. The interesting fact about cards games is

that peoples wants to play more whether they win or lose. So from this ia I

will investigate why casino owners are always in prot! I am also going to

deal with the usage of probability and e"pectatio

n in our daily life.

Introduction

#robability$ how likely some event will happen.

#robab

ility of an event happening%

First, I will establish that the group I want to study is specifically junior IB Theory of Knowledge (TOK) students at my school. In that group, there are 83 students that I will observe. There are two TOK teachers that all meet with students during Learning Lab, or study hall, the second to last block of the school’s schedule; one meets on Mondays and Wednesdays and the other on Tuesdays and Thursdays. For this reason, I will travel during Learning Lab on a Monday to the two teachers of the TOK classes and again on the following day. If some students are absent those two days, I will take the time to collect their information on Wednesday and/or Thursday during Learning Lab, and if need be, I will continue my investigation the following week, since TOK classes do not meet on Fridays.

After the schedule is decided, I will create a chart for each of the two classes that records the number of people with the following hair and eye color. Both of the charts will look like this:

I will then set out to each of the classes to obtain my data in tally marks until all 83 students have been studied. If I find students with hazel-colored eyes (a combination of green and brown) I will ask them which color they identify with more. After all information has been collected I will add up the data and combine the two charts into one, then I will conduct a *χ*2 to decide if eye color is dependent on hair color using a table of critical values of the *χ*2 distribution with two degrees of freedom (df) and 5% level of significance. The critical value for two degrees of freedom and 5% level of significance is 5.991, so if my *χ*2 value is less than 5.991, I will accept the null hypothesis, that the factors are independent, but if the *χ*2 value is greater than 5.991, I will reject the null hypothesis and accept the alternative hypothesis, that the factors are dependent.

`No one is immune from addiction; it afflicts people of all ages, races, classes, and professions. Patrick J. Kennedy`

The following are examples of HL/SL IAs based on the current mark scheme with grader comments. Please note that difference between HL and SL IAs is the level of math expected of students which is reflected in slightly different rubrics and consequently the HL and SL grades differ slightly.

Below are the grades for each IA and the rationales behind the grade received.

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