Independent vs mutually exclusive events: Venn diagram exam question | IB Math AA

IB Mathematics AA and AI tutoring with Pietro Meloni: https://www.pietromeloni.com/subjects... P(A ∩ B) = 0.21 and P(A′ | B′) = 0.7. From the Venn diagram P(A) = 0.09 + x and P(B) = 0.49 + x; independence gives x = (0.09 + x)(0.49 + x), a quadratic with discriminant zero, so x = 0.21. Independent does not mean mutually exclusive: setting x = 0 contradicts itself. Watch it ad-free with the written answer: https://www.pietromeloni.com/worked-s... Chapters 00:00 The mistake that costs the most marks 00:31 The question: IB Math AA HL, Paper 2, 6 marks 01:12 Draw the Venn diagram first 01:47 What independent means: P(A ∩ B) = P(A)P(B) 02:18 Three equations from the diagram 02:53 The quadratic, and a discriminant of zero 03:18 x = 0.21, and the check 03:43 Independent is not mutually exclusive 04:17 Part b: conditional probability, 0.7 04:53 The shortcut: complements are independent too 05:19 A question for you 05:43 Three things to take into the exam I'm Pietro Meloni, PhD in Physics, and I tutor IB Mathematics (AA and AI, SL and HL) and IB Physics online, one to one. Every video takes one real exam-style question apart, step by step, the way I do it with my students. Free IB past paper library: https://www.pietromeloni.com/past-pap... 1:1 online IB Maths and Physics tutoring with Pietro Meloni: https://www.pietromeloni.com/?utm_sou... Question in the style of IB Mathematics AA HL, Paper 2, May 2022, Question 5, rewritten in my own words with the figure redrawn. Not affiliated with or endorsed by the International Baccalaureate Organization. IB is a trademark of its owner. All questions have been rewritten and all figures redrawn. #IBMathAA #Probability #PietroMeloni