2025 MI P2 Q8
2025 MI P2 Q8
8 marks
For events \(A\) and \(B\), it is given that \(\mathrm{P}(A) = \frac{11}{20}\), \(\mathrm{P}(A \cup B) = \frac{4}{5}\) and \(\mathrm{P}(B|A) = \frac{4}{11}\).
- Find
- \(\mathrm{P}(B)\),[3]
- \(\mathrm{P}(A \cap B')\).[1]
- Determine if the events \(A\) and \(B'\) are mutually exclusive.[1]
A third event \(C\) is such that \(\mathrm{P}(C) = 0.6\) and \(B\) and \(C\) are independent.
- Find \(\mathrm{P}(B \cap C)\).[1]
- Find the range of values of \(\mathrm{P}(A \cap B' \cap C)\).[2]
Video Solution:
Video solution locked
A free account saves your progress; this video needs tuition enrolment.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs tuition enrolment.
Create a free account to practise similar questions.
Answer:(i)(a) \(\mathrm P(B)=\dfrac9{20}\) (b) \(\mathrm P(A\cap B')=\dfrac7{20}\) (ii) Not mutually exclusive (iii) \(\mathrm P(B\cap C)=0.27\) (iv) \(0.13\leq\mathrm P(A\cap B'\cap C)\leq0.33\)
Need help? Join our JC Math tuition classes.
Learn more