(i) The probability that Mohit goes to the cinema is 0.35. The probability that he spends less than $50 at the cinema is 1 - 0.8 = 0.2. Therefore, the probability that Mohit will go to the cinema and spend less than $50 is:

\(P(C \cap <50) = 0.35 \times 0.2 = 0.07\)

(ii) We need to find \(P(C \mid <50)\), the probability that Mohit went to the cinema given that he spent less than $50. This is given by:

\(P(C \mid <50) = \frac{P(C \cap <50)}{P(<50)}\)

We already found \(P(C \cap <50) = 0.07\).

Now, calculate \(P(<50)\):

\(P(<50) = P(S \cap <50) + P(C \cap <50) + P(H \cap <50)\)

\(P(S \cap <50) = 0.25 \times (1 - 0.7) = 0.25 \times 0.3 = 0.075\)

\(P(C \cap <50) = 0.07\)

\(P(H \cap <50) = 0.4 \times 1 = 0.4\)

Thus, \(P(<50) = 0.075 + 0.07 + 0.4 = 0.545\)

Therefore, \(P(C \mid <50) = \frac{0.07}{0.545} = 0.128\) (or \(\frac{14}{109}\))