Lottery tickets numbered consecutively from $100$ through $999$ are placed in a box. Jack picked up one ticket from

Lottery tickets numbered consecutively from $100$ through $999$ are placed in a box. Jack picked up one ticket from the box, noted the number, and put the ticket back in the box. Then Rose came and did the same. If both picked tickets where all the digits within the picked number are distinct and prime, then find the probability that the sum of the two ticket numbers is odd?

A. $\dfrac1{150\cdot 50}$

B. $\dfrac2{150\cdot 50}$

C. $\dfrac1{54}$

D. $\dfrac1{27}$

E. $\dfrac38$

Answer: E

Source: e-GMAT

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