A botanical research team is investigating the presence of two rare genetic markers, G1 G_1\,G1 and G2G_2G2, in a specific orchid population. The events A A\,A and B B\,B are defined as an orchid having marker G1 G_1\,G1 and G2 G_2\,G2 respectively, where
P(A)=p,P(B)=q,P(A∪B)=0.7,P(B∣A)=0.2 P(A) = p, \quad P(B) = q, \quad P(A \cup B) = 0.7, \quad P(B|A) = 0.2 P(A)=p,P(B)=q,P(A∪B)=0.7,P(B∣A)=0.2Show that
4p+5q=3.5 4p + 5q = 3.5 4p+5q=3.5A third genetic marker, G3G_3G3, is represented by event CCC. It is known that B B\,B and C C\,C are mutually exclusive events such that
P(B∪C)=0.85,P(C)=12p+q P(B \cup C) = 0.85, \quad P(C) = \frac{1}{2}p + q P(B∪C)=0.85,P(C)=21p+q(i) Find a second equation in p p\,p and qqq.
(ii) Hence determine the values of p p\,p and qqq.
Determine whether or not the presence of marker G1 G_1\,G1 and marker G2 G_2\,G2 are statistically independent. Justify your answer.
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.