Section C
Long Duestions
(lotal 45 oxart)
Answer AlL questions ia this section. caly four passible alticsion affering place ty the tmuitate for peri acnderac ycas The protability of four porsible adaivition affering Nascs ase reased is the fallowing toblo.
\begin{tabular}{|c|c|c|c|c|}
\hline Offering nloces & 47000 & 48000 & 49000 & 50060 \\
\hline Protobility & 0.15 & 0.40 & 0.25 & \( \mathbf{X} \) \\
\hline
\end{tabular}
(i) What ts the valuo of " \( \mathbf{X}^{-} \)in the uble obove?
(2 carks)
(ii) What is the expectod oflering place for the instiuae?
(3 matis)
(b) Threc athleter, \( X, Y \) and \( Z \), cacb shoot a a usget in a cormecuion. The probebili of hitling the wrgel by \( X, Y \) and \( Z \) are \( \frac{2}{3}, \frac{3}{4} \) and \( \frac{4}{5} \) respectivel).
(Correct your answers to 4 decitial places or in f?raction.)
(i) Find the probability that all three athletes mis the aurget.
(ii) Find the probabilisy that only two athictos his the tirgel
(iii) Find the probability that as lenst one ethlete cuuld bit the \( Q \) mar targel
(iv) If beso three athletes shwot at a target scquentialh, what is Be probability that ondy \( Y \) could hil tho target? (Hiat \( X \) shoot first, then \( Y \) shoo and firsally \( Z \) will ahoot.)
(Total \( 16 \mathrm{mar} \)
