please show work A university study has found that 85 of the

please show work

A university study has found that 85% of their students pass their Spanish course. Of the students who pass,80% had taken a foreign language in high school. The study also indicates that of the students who did not pass Spanish, 25% had taken a high school foreign language. Given that a randomly selected student did not take a foreign language in high school, what is the probability that the student will pass Spanish at the university? Show how you get your answer.

Solution

We need to calculate

P( Student will pass Spanish/Student did not take foreign language in high school)

P(Student did not take foreign language in high school) = 0.85*(1-0.80)+0.15*(1-0.25) = 0.2825

P( Student will pass Spanish/Student did not take foreign language in high school) =(0.85*(1-0.80))/0.2825

P( Student will pass Spanish/Student did not take foreign language in high school) = 0.60177