A certain form of cancer is known to be found in women over 60 with probability 0.07. A blood

test exists for the detection of the disease, but the test is not

infallible. In fact, it is known that

10% of the time the test gives a false negative (i.e., the test incorrectly gives a negative result)

and 5% of the time the test gives a false positive (i.e., incorrectly gives a positive result). If a

woman over 60 is

known to have taken the test and received a favourable (i.e., negative) result,

what is the probability that she has the disease?