
Basic Probability
8) Of the 200 students studying VCE at Merlynston Secondary College, 80 study Maths Methods , while there are 65 Physics students. If there are 85 students who don't take either Maths Methods or Physics, find the probability that a randomly selected student:
d) studies Maths Methods and Physics
e) studies Physics, given that the stuent studies Maths Methods.
Any help would be appreciated!

Of 200 students 80 study math, so 120 do not study math. You have been told that 85 students study neitrher physics nor math, so that means that 12085 = 35 study physics but not math.Since 65 study physics, that means that 6535 = 30 study both physics and math. And finally, since 80 study math, and you know that 20 study math and physics, then 8030=50 study math but not physics.
So:
d) the prob that a student studies math and physics is 30/200.
e) the probability that a student studies physics given that he studies math is 30/80. Or you could apply Bayes: P(physics  math) = P(physics & math)/P(math) = (30/200)/(80/200) = 3/8.