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01 Hours 30 Minutes

80 Marks

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IB MATH AI SL, Paper 2, November, 2021, TZ0, Solved Past Paper

Master the 2021 IB November for Paper 2 Mathematics AI SL with examiner tailored solutions and comments for TZ0

Question 1 [Explained]

This question involves analyzing data collected from a survey of 1280 students regarding their preferred electronic devices. The data is categorized by age groups: 11-13, 14-16, and 17-18 years old. The table provided summarizes the preferences for laptops, tablets, and mobile phones across these age groups. The task is to calculate probabilities related to these preferences and age groups, as well as to conduct a chi-squared test to determine if there is a significant association between age and device preference.

The table is structured with rows representing the devices and columns representing the age groups, along with a total column. The total number of students in each age group and the total number of students preferring each device are also provided. This setup allows for the calculation of probabilities and the application of statistical tests.

Preferred device	11-13	14-16	17-18	Total
Laptop	143	160	153	456
Tablet	205	224	131	560
Mobile phone	72	128	64	264
Total	420	512	348	1280

Question 1 [a] [Explanation]

This part of the question requires calculating probabilities related to the preferences of students for different electronic devices. The probabilities are based on the data provided in the table, and each subpart focuses on a specific condition or combination of conditions.

Question 1 [a] [i] [Explanation]

Calculate the probability that a randomly chosen student from the group prefers a tablet. This involves finding the ratio of students who prefer tablets to the total number of students surveyed.

Question 1 [a] [ii] [Explanation]

Calculate the probability that a randomly chosen student is 11-13 years old and prefers a mobile phone. This involves finding the ratio of students in this specific category to the total number of students surveyed.

Question 1 [a] [iii] [Explanation]

Calculate the probability that a student prefers a laptop given that they are 17-18 years old. This requires finding the conditional probability based on the data provided.