From Computational Statistics (CSE383M and CS395T)
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Segment 1. Let's Talk about Probability


To Calculate

1. Prove that <math>P(ABC) = P(B)P(C|B)P(A|BC)</math>

We know from Conditional Probability that, <math>P(B|A) = \frac{P(AB)}{P(A)}</math>

<math>\begin{align}P(B)P(C|B)P(A|BC) &= P(B)\text{ }\frac{P(BC)}{P(B)}\text{ }\frac{P(ABC)}{P(BC)}\\

&= P(ABC)\end{align}</math>

2. What is the probability that the sum of two dice is odd with nether being a 4?