4.87 Does knowledge lead to the decision to be an engineer? To investigate this question, Hamill and Hodgkinson (Proceedings of ICE, 2003) surveyed 566, 11–16-year-olds, and classified them by their level of knowledge about engineering and the likelihood of becoming an engineer. The results are listed in Table 4.33.

a Find the probability that a randomly selected respondent said it was very unlikely that he or she will become an engineer.

b Find the probability that a randomly selected respondent knew nothing about engineering given that the respondent said it is very unlikely that he or she will become an engineer.
c Hamill and Hodgkinson concluded, “Lack of knowledge corresponds to engineering being an unlikely career, whereas knowledge makes it more likely.” Can we make this conclusion from the data collected? Justify your answer.