Let \(A\) be the event that Jamie attends the training session, and \(T\) be the event that Jamie is chosen for the team.

Given: \(P(A) = 0.5\), \(P(T|A) = 1\), \(P(T|A^c) = 0.6\).

(i) The probability that Jamie is chosen for the team is:

\(P(T) = P(T|A)P(A) + P(T|A^c)P(A^c) = 1 \times 0.5 + 0.6 \times 0.5 = 0.5 + 0.3 = 0.8\)

(ii) The conditional probability that Jamie attended the training session, given that he was chosen for the team, is:

\(P(A|T) = \frac{P(T|A)P(A)}{P(T)} = \frac{1 \times 0.5}{0.8} = \frac{0.5}{0.8} = 0.625\)

Thus, \(P(A|T) = 0.625\) or \(\frac{5}{8}\).