5 Playground equipment consists of swings ( \(S\) ), roundabouts ( \(R\) ), climbing frames ( \(C\) ) and play-houses \(( P )\). The numbers of pieces of equipment in each of 3 playgrounds are as follows.
| Playground \(X\) | Playground \(Y\) | Playground \(Z\) |
| \(3 S , 2 R , 4 P\) | \(6 S , 3 R , 1 C , 2 P\) | \(8 S , 3 R , 4 C , 1 P\) |
Each day Nur takes her child to one of the playgrounds. The probability that she chooses playground \(X\) is \(\frac { 1 } { 4 }\). The probability that she chooses playground \(Y\) is \(\frac { 1 } { 4 }\). The probability that she chooses playground \(Z\) is \(\frac { 1 } { 2 }\). When she arrives at the playground, she chooses one piece of equipment at random.
- Find the probability that Nur chooses a play-house.
- Given that Nur chooses a climbing frame, find the probability that she chose playground \(Y\).