Level 1 - Quantitative Method - Probability

Probability

Basic rules of probability

1.      P(AB) = P(A) * P(B)  if A & B are independent

 P(AB) = P(A∣B) * P(B)  if A & B are not independent

       If P(A∣B) = P(A) à A & B are independent event

2.      P(A∣B) = P(AB)/P(B)

3.      P(A or B) = P(A) + P(B) – P(AB)

      ※P(AB) = 0 if A & B are mutually exclusive

4.      Total Probability Rule:

      假設 A 不是 independent event
       P(A) = P(AB₁) + P(AB₂) + …… + P(AB_N); or
      P(A) = P(A∣B₁) + P(A∣B₂) + …… + P(A∣B_N)

Computing correlation with calculator

Steps:

1.       2ND   7  (DATA)

2.      習慣先 clear memory à  2ND   CElC

3.      ↑   ↓  input data à X = 第一組 observation 的值 ; Y = 第二組 observation 的值

4.       2ND   8  (STAT)

5.      Set mode à  2ND   ENTER  (SET) à Lin (Linear)

6.      ↑   ↓  可顯示有關 Data 的:

                 - No of observation
                 - Mean and S.D. of observation set 1 & 2
                 - r 就是 correlation

Bayes Formula (Updated Probability)

Example:

Given P(A∣B), P(B) & P(A) à Find P(B∣A)
P(B∣A) = P(A∣B) * P(B) / P(A)
※可能要行用total probability rule去計算P(A)
     P(A) = P(A∣B₁) + P(A∣B₂) + …… + P(A∣B_N)

Combination (nCr) vs. Permutation (nPr)

- Use nCr if order isn’t a concern
- Use nPr if order is a concern