The events AAA and BBB satisfy
P(A)=x,P(B)=y,P(A∪B)=0.72,P(B∣A)=0.2 P(A) = x, \quad P(B) = y, \quad P(A \cup B) = 0.72, \quad P(B|A) = 0.2 P(A)=x,P(B)=y,P(A∪B)=0.72,P(B∣A)=0.2Show that
4x+5y=3.6 4x + 5y = 3.6 4x+5y=3.6The events BBB and CCC are mutually exclusive such that
P(B∪C)=0.9,P(C)=14x+y P(B \cup C) = 0.9, \quad P(C) = \frac{1}{4}x + y P(B∪C)=0.9,P(C)=41x+y(i) Find a second equation in xxx and yyy.
(ii) Hence find the value of xxx and the value of yyy.
Determine whether or not AAA and BBB are statistically independent. You must show your working clearly.
200 exam-style questions on OCR (MEI) A Level Maths 2.3 Probability, covering 2.3.1 Calculate the probability of an event, 2.3.2 Complementary events, 2.3.3 Expected frequency of an event, 2.3.4 Diagrams to calculate probabilities, 2.3.5 Mutually exclusive and independent events, 2.3.6 Add probabilities for mutually exclusive events, 2.3.7 Multiply probabilities for independent events, 2.3.8 Mutually exclusive and independent events (notation) (A-level only), 2.3.9 Venn diagrams for probabilities (A-level only), 2.3.10 Conditional probabilities (A-level only), and 2.3.11 Independence via conditional probability (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.