Probability Question GRR

[kenhung123]

A study has been conducted on the Semester 1 and 2 exam results of Year 11 Maths Methods students at University High School over the last 10 years. It has been found that if a student passed the Semester 1 Exam he has 1 95% chance of passing the Semester 2 Exam. However, if he fails the Semester 1 Exam, there is a 70% chance that he will also fail the Semester 2 Exam. Assume that in 2008 15% of the students failed the Semester 1 Exam.

Given that Andrew passes the Semester 2 Exam, what was the probability that he failed the Semester 1 Exam?

Use a tree diagram to solve this question.

[nala]

Okay, firstly, this is a conditional probability question.

Let S1 and S2 equal semester 1 and 2. P=pass, F=fail.

We need Pr(F(S1)|P(S2)) = Pr(F(S1)P(S2)) / Pr(P(S2))

Using the attached tree diagram, Pr(F(S1)P(S2))= 0.15*0.3= 0.045
Pr(P(S2))= PP + FP = (0.85*0.95) + (0.15*0.3) = 0.8075 + 0.045 = 0.8525

Thus, 0.045/0.8525 = 0.05279

I hope that's correct! If not, I'll see if I can figure out where I went wrong

[lachymm]

kenhung you in year 11 yeah?
You pretty far into the course man!