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!
September 10th 2010, 10:57 AM
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 120-85 = 35 study physics but not math.Since 65 study physics, that means that 65-35 = 30 study both physics and math. And finally, since 80 study math, and you know that 20 study math and physics, then 80-30=50 study math but not physics.
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.