A survey records the number of students enrolled in $3$ different types of courses and at $2$ different levels at a university. If a student is selected at random, what is the probability that the student is at the postgraduate level and enrolled in arts?

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If $P(\text{rain}\mid \text{traffic})$ is written, it represents the probability of _______________ given _______________.

A university records the number of first-time and returning students who passed or failed a final exam. The data is as follows:

What is the probability that a student passed, given that the student was returning?

A statistics department reports the following data for students taking the final exam:

What is the probability that a student was a repeat test taker, given that the student failed the exam?

A hospital surveyed $1,000$ staff members — $500$ nurses and $500$ doctors — to find out whether they participate in wellness programs. The results are shown in the table below:

What is the probability that a randomly selected staff member participates in wellness programs, given that the staff member is a doctor?

A college tracks the number of male and female students who received bachelor's degrees in science and non-science fields in a given year:

What is the probability that a randomly selected bachelor's degree recipient earned a science degree, given that the student is male?

A college tracks the number of male and female students who graduate with degrees in science and non-science fields:

What is the probability that a randomly selected science graduate is male?