If you are a typical subject, your would have answered between 0.7 and 0.8. The answer is in fact, 0.96, which can be computed as shown here .
Bayes' is a formally optimum rule about how to revise opinions in the light of evidence. Typically subjects revise their probabilities less than Bayes's rule suggests. We are "conservative" processors of information.
It seems that the major cause of conservatism is human misaggregation of the data. We perceive each datum accurately and are aware of it's individual diagnostic meaning, but are unable to combine its diagnostic meaning well with the diagnostic meaning of other data when revising opinions.