Complete the tree diagram below.

Find the value of \(p\).

     (A1)(A1)     (C2)

Note:     Award (A1) for each correct pair of probabilities.

[2 marks]

\(\frac{4}{5}p + \frac{1}{5} \times \frac{1}{4} = \frac{3}{5}\)     (A1)(ft)(M1)(M1)

Note:     Award (A1)(ft) for two correct products from part (a), (M1) for adding their products, (M1) for equating the sum of any two probabilities to \(\frac{3}{5}\).

\((p = ){\text{ }}\frac{{11}}{{16}}{\text{ }}(0.688,{\text{ }}0.6875)\)    (A1)(ft)     (C4)

Note:     Award the final (A1)(ft) only if \(0 \leqslant p \leqslant 1\). Follow through from part (a).

[4 marks]