MATHS - 概率一題

條件prob. 就係given一d情況, 再求以後會發生某事o既機會
除a係因為 你而家個範位細左, 變左o係a之內, 所以你個總prob. 會大左(a>1, 除a會大左)

唔好搞錯條式p(a/b)=p(a & b)/ p(b)
所以用
p(maths/phy)=p(phy & maths)/p(phy)
=0.15/0.3
=0.5

自己試做(b)
(b)=0.75

Let H={students that fail in physics} //假設H為物理不合格的學生
and M={students that fail in math} //同M為數學不合格的學生
Given P(H)=0.3, P(M)=0.2, P(H & M)=0.15

a. if the student fails in physics, find the probability that he fails in maths as well
呢題即係要搵 P(the student fails in maths given that he fails in physics)
P(M | H) = P(M & H)/P(H) = 0.15/0.3 = 0.5

b. if the student fails in maths, find the probability that he fails in physics as well
呢題即係要搵 P(the student fails in physics given that he fails in math)
P(H | M) = P(H & M)/P(M) = 0.15/0.2 = 0.75

More about conditional probability:
P(A & B) = P(A|B)*P(B) = P(B|A)*P(A)
if A and B are independent, P(A & B)=0 (since P(A|B)=P(B|A)=0)
P(A) = P(A & B) + P(A & B') = P(B|A)*P(A) + P(B'|A)*P(A)
[or P(B|A) + P(B'|A) = 1]

A)3/20
B)3/20