Let s be the chance of success for a single 30 second period
Let n be the number of 30 second periods
Let t be the total chance of success over all periods

1 - (1 - s)^n = t

(1 - s)^n = 1 - t
ln( (1 - s)^n ) = ln(1 - t)
n * ln(1 - s) = ln(1 - t)
n = ln(1 - t) / ln(1 - s)

n = ln(1 - 0.5) / ln(1 - 0.003)
  = ln(0.5) / ln(0.997)
  ≈ 230.7