Solutions - 5050-04

Let $A$ = syntax error, $B$ = logic error.

(1) Find $P[A]$ and $P[B]$:

$$P[B]=\frac{P[A\cap B]}{P[A|B]}=\frac{0.16}{0.4}=0.4P[A]=\frac{P[A\cap B]}{P[B|A]}=\frac{0.16}{0.5}=0.32$$

---

(2) Check the independence condition:

$$P[A]\cdot P[B]=0.32\cdot 0.4=0.128\ne 0.16=P[A\cap B]\Rightarrow \text{NOT independent}$$