4．A bag contains 64 coloured beads．There are \(r\) red beads，\(y\) yellow beads and 1 green bead and \(r + y + 1 = 64\) Two beads are selected at random，one at a time without replacement．
（a）Find the probability that the green bead is one of the beads selected． The probability that both of the beads are red is \(\frac { 5 } { 84 }\)
（b）Show that \(r\) satisfies the equation \(r ^ { 2 } - r - 240 = 0\)
（c）Hence show that the only possible value of \(r\) is 16
（d）Given that at least one of the beads is red，find the probability that they are both red．