Probability - Probability Bounds and Inequalities
Probability - Probability Bounds and Inequalities
9 marks
The events \(A\) and \(B\) satisfy \(P(A)=\dfrac{2}{5}\), \(P(B')=\dfrac{3}{4}\) and \(P(B\mid A)=\dfrac{1}{4}\).
- Find \(P(A'\cap B')\) and hence prove that the events \(A'\) and \(B'\) are independent.[4]
A third event \(C\) satisfies \(P(C)=\dfrac{1}{2}\) and \(P(A\cap B\cap C)=\dfrac{1}{20}\). It is also known that \(B\) and \(C\) are independent, while \(A\) and \(C\) are not independent.
- Find the range of possible values of \(P(A'\cap B'\cap C')\).[5]
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) \(P(A'\cap B')=\dfrac{9}{20}\); \(A'\) and \(B'\) are independent. (ii) \(\dfrac{3}{40}\le P(A'\cap B'\cap C')\le\dfrac{3}{8}\), with \(P(A'\cap B'\cap C')\ne\dfrac{9}{40}\).
Need help? Join our JC Math tuition classes.
Learn more