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.
