Question $3$

$($i$)$ Figure $1$ below illustrates the Fault Tree Analysis used to investigate the root causes of the wrong raw material being added to a bioreactor. The following potential root causes and their corresponding probabilities of occurrence were identified:

$\backslash$table$[[$Potential root cause,$\backslash$table$[[$Probability$],[$of occurrence$]]],[$Management system failure,$0\mathrm{.}01],[$Equipment failure,$0\mathrm{.}05],[$Human error #$3,0\mathrm{.}30],[$Labelling procedure inadequate,$0\mathrm{.}20]]$

$\backslash$table$[[$Potential root cause,$\backslash$table$[[$Probability$],[$of occurrence$]]],[$Human error #$2,0\mathrm{.}10],[$Arrival$-$check procedure inadequate,$0\mathrm{.}25],[$Human error #$1,0\mathrm{.}15]]$

Calculate the probability of the wrong raw material being added to the bioreactor. $(6$ marks$)$

Figure $1-$ Fault Tree Analysis for introducing the wrong chemical to a tank