IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Static and Probability–Mutually exclusive events
Topic :Static and Probability- Weightage : 21 %
All Questions for Topic : Sampling techniques,Data manipulation and misinterpretation,Graphical representations (including: bivariate graphs, scatter graphs, box plots, cumulative frequency graphs)
,Lines of best fit,Data processing: quartiles and percentiles,Measures of dispersion: interquartile range,Correlation, qualitative handling,Relative frequency,Response rates,Sets, including notation and operations up to three sets,Probability with Venn diagrams, tree diagrams and sample spaces,Mutually exclusive events,Combined events
Question (5 Marks)
A group consisting of 120 students from MYP year 1 and MYP year 5 chose their favourite freetime activity from the following list: playing sport, gaming, and interacting on social media. Their choices have been organized in the table below.
Question (a) : 1 marks
A student is selected at random from MYP year 5 . Write down the probability that this student chose gaming as their favourite activity.
▶️Answer/Explanation
Ans:
The probability that a student selected at random from MYP year 5 chose gaming as their favorite activity is given by:
\[ \text{Probability} = \frac{\text{Number of students who chose gaming in MYP year 5}}{\text{Total number of students in MYP year 5}} \]
Plugging in the values:
\[ \text{Probability} = \frac{16}{48} = \frac{1}{3} \]
Hence, the probability that a student selected at random from MYP year 5 chose gaming as their favorite activity is \( \frac{1}{3} \).
Question (b) : 2 marks
Examine the following statement:
“MYP year 1 and MYP year 5 students are equally likely to choose gaming as their favourite activity.”
▶️Answer/Explanation
Ans:
To examine the statement “MYP year 1 and MYP year 5 students are equally likely to choose gaming as their favorite activity,” we need to compare the probabilities of choosing gaming in both MYP year groups.
From the given table, we can see that in MYP year 1, 16 students chose gaming as their favorite activity out of a total of 72 students. Therefore, the probability of choosing gaming in MYP year 1 is:
\[ \text{Probability in MYP year 1} = \frac{16}{72} = \frac{2}{9} \]
Similarly, in MYP year 5, 16 students chose gaming as their favorite activity out of a total of 48 students. The probability of choosing gaming in MYP year 5 is:
\[ \text{Probability in MYP year 5} = \frac{16}{48} = \frac{1}{3} \]
Comparing the probabilities, we can see that \( \frac{2}{9} \neq \frac{1}{3} \). Therefore, the statement “MYP year 1 and MYP year 5 students are equally likely to choose gaming as their favorite activity” is not true. The probabilities of choosing gaming differ between the two year groups.