A language centre offers French and Spanish courses. The two-way table shows the numbers of male students and female students on each course.
French
Spanish
Total
Male
31
27
58
I
Female
46
16
62
Total
77
43
120
One student is chosen at random.
Federico says that the probability that they are male given that they study Spanish is 23.
Explain why Federico is correct.

Anew test for ra is being developed. the test is administered to 750 patients with ra and 750 without ra. for the sake of the question, assume the prevalence of ra in this population is 50%. of the 750 patients with ra, 575 have a positive result. of the 750 patients without ra, 150 have a positive result. what is the positive predictive value of the new test? a575/(575+150) b. 600/(600+ 150) c. 575/(575+125) d. 600/(600+ 125)