I recently failed to solve a problem relating to conditional expectation. The problem states:

A student is initially outside. He is given the choice with a probability of 0.4 of going to the playground, 0.3 of shopping in the mall and 0.3 of returning home. If he is in the playground, he takes 2 hrs of time and then decides to stay in the playground again or return back home. (he can continue to decide to stay in playground like a recursive process) Similarly, If he is in the mall, he takes 3 hrs of time and then decides to stay in the mall again or return back home. (he can continue to decide to stay in mall like a recursive process) For all cases, it takes 1 hr to return home. what is the expected hours the student was outside home?

Initially, I thought about using Law of Total Expectation here. Like:

E[x] = E[x|y=1] x P(y=1) + E[x|y=2] x P(y=2) + E[x|y=3] x P(y=3)

x = total # hrs outside, y = choice.

But I don't know how to handle the conditional expectations for each of the individual statistical event. For instance, the case where students stays in the playground, is my equation correct? E[x|y=1] = 2 + 1/(0.4) . Similarly for staying in mall? E[x|y=2] = 3 + 1/(0.3)

Or am I making some very basic errors? Help would be appreciated.