IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Static and Probability–Probability with Venn diagrams
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 (8 Marks)
One of four main blood types can be found in a human body. They are known as $\mathbf{A}, \mathbf{B}, \mathbf{A B}$ and $\mathbf{O}$. Each blood type can be further classified as either a Rhesus positive (+) or Rhesus negative $(-)$.
For example, a possible combination is blood type $\mathbf{O}$ and Rhesus negative which is written as $\mathbf{O}$ –
The pie charts below shows the distribution of the blood types and Rhesus types for a blood donor centre recorded in 2019.
Question (a) : 2 marks
People with blood type $\mathbf{O}-$ are known as universal donors. They can donate their blood to patients with any blood type.
Show that the probability that a randomly selected person has blood type $\mathbf{O}-$ is 0.1 .
▶️Answer/Explanation
Ans:
Given that people with blood type $\mathbf{O}-$ are considered universal donors, we can make an assumption that they are evenly distributed across all blood types. This means that the percentage of individuals with blood type $\mathbf{O}-$ is proportional to the percentage of people with blood type $\mathbf{O}$. Since the exact percentage for blood type $\mathbf{O}$ is not provided, we can assume it is the remaining percentage after subtracting the other blood types:
Blood type $\mathbf{O}: 100\% – (44\% + 11\% + 5\%) = 40\%$
Now, we can calculate the probability of a randomly selected person having blood type $\mathbf{O}-$:
Probability of blood type $\mathbf{O}- = \text{Probability of blood type}\mathbf{O-}\times \text{Probability of Rhesus negative (-)}$
Probability of blood type $\mathbf{O}- = 40\% \times 25\% = 0.4 \times 0.25 = 0.1$
Therefore, the probability that a randomly selected person has blood type $\mathbf{O}-$ is $0.1$ or $10\%$.
Question (b) : 1 marks
Hence, find the coordinates $(x, y)$ of points $\mathrm{A}$ and $\mathrm{B}$.
▶️Answer/Explanation
Ans:
To determine the expected number of people that have blood type $\mathbf{O}-$ among the 30 people donating blood, we need to consider the probability of each person having that blood type.
From the previous answer, we found that the probability of a randomly selected person having blood type $\mathbf{O}-$ is 0.1 or $10\%$.
The expected number of people with blood type $\mathbf{O}-$ can be calculated by multiplying the probability of each person having that blood type by the total number of people donating blood.
Expected number of people with blood type $\mathbf{O}- = \text{Probability of blood type }\mathbf{O}- \times\text{Total number of people donating blood}$
Expected number of people with blood type $\mathbf{O}- = 0.1 \times 30 = 3$
Therefore, the expected number of people that have blood type $\mathbf{O}-$ among the 30 people donating blood is 3.