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A random number generator that returns an integer is run twice. The notation for conditional probability is P(even on 2nd run|odd on 1st run) .

Which notation is the probability of the two events being not independent?

Choices

​ P(even on 2nd run|odd on 1st run)=P(even on 2nd run) ​

​ ​P(even on 2nd run|odd on 1st run)=P(odd on 1st run and even on 2nd run)/P(odd on 1st run) ​ ​

​ P(even on 2nd run|odd on 1st run)=P(odd on 1st run)/P(even on 2nd run) ​

​ ​P(even on 2nd run|odd on 1st run)=P(even on 2nd run)/P(odd on 1st run) ​​

Dec 20, 2018

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$$\text{so much text...}\\ A = \{\text{even on 2nd run}\}\\ B = \{\text{odd on 1st run}\}\\ \text{Choices}\\ P[A|B] = P[A]\\ P[A|B] = \dfrac{P[B\cap A]}{P[B]}\\ P[A|B] = \dfrac{P[B]}{P[A]}\\ P[A|B] = \dfrac{P[A]}{P[B]}$$

1) is true if A and B are independent

2) is always true

3) may or may not be true depending on A and B, it being true doesn't say anything about independence of A and B

4) if A and B are independent then P[A|B] = P[A], and thus this choice shows A and B are not independent

Dec 20, 2018