Chance of Positron Escaping an Atom

Suppose a positron was created in the nucleus of the atom. Now, suppose we have 1,000,000 of these atoms all in their own vacuum. Statistically, would a large percent of positrons successfully leave these atom without being annihilated by an electron? Assume we have an element such as Sodium-22. Say we have billions of atoms surrounding each atom, are the chances still low or high for a positron to escape?

• Presumably this is roughly the same as a 250keV positron-sodium atom collision resulting in annihilation of the positron – John Rennie Jun 12 '14 at 7:39
• Same thought as John's : just reverse the problem to calculate the probability of an exoatomic $\beta+$ reaching the nucleus. – Carl Witthoft Jun 12 '14 at 11:49