(a)[2]
Complete the tree diagram below.
(b)[1]
Write an expression, in terms of $n$, that gives the probability that Esther’s first ball is red and her second ball is green.
(c)[2]
The probability that Esther’s first ball is red and her second ball is green is $\frac{1}{7}$. Show that $n^2 - 36n + 180 = 0$.
(d)[2]
Solve the equation $n^2 - 36n + 180 = 0$. Show all your working.
(e)[3]
There are more green balls than red balls in the bag. Find the probability that Esther takes two green balls. Give your answer as a fraction in its lowest terms.