From 10±year-old memories:
Draw up a 2x2 table. The columns represent testing positive and testing negative; the rows represent having cancer and not. We will work with probabilities in each cell, although using cardinalities from a population of, say, 10000 will yield whole numbers throughout, which some may find easier.
Statement 1 tells us that the row totals are in the proportion of 1:99.
Statement 2 tells us that in row 1, the columns are in the proportion of 80:20.
We know that row 1 sums to 0.01, so row 1 is 0.008 | 0.002.
Statement 3 tells us that in row 2, the columns are in the proportion of 9.6:(100-9.6).
We know that row 2 sums to 0.99, so row 2 is 0.09504 | 0.8946
We have the complete table. And the figure we are asked for is, given we are in column 1, what is the probability we are in row 1. This is (row 1, column 1) / [(row 1, column 1) + (row 2, column 1)] (*), or
0.008 / (0.008 + 0.09504)
= 0.008 / 0.10304
= 25/322 ~= 7.76 %
(*) This is Bayes Theorem, right? P(A | B) = P(A B) / P(B) ?