Find the mean number of defective switches in the sample.

Find the probability that there are exactly six defective switches in the sample.

Find the probability that there is at least one defective switch in the sample.

evidence of binomial distribution (may be seen in parts (b) or (c))     (M1)

e.g. np, \(100 \times 0.04\)

\({\text{mean}} = 4\)     A1     N2

[2 marks]

\({\rm{P}}(X = 6) = \left( {\begin{array}{*{20}{c}}
{100}\\
6
\end{array}} \right){(0.04)^6}{(0.96)^{94}}\)     (A1)

\( = 0.105\)     A1     N2

[2 marks]

for evidence of appropriate approach     (M1)

e.g. complement, \(1 - {\rm{P}}(X = 0)\)

\({\rm{P}}(X = 0) = {(0.96)^{100}} = 0.01687 \ldots \)     (A1)

\({\rm{P}}(X \ge 1) = 0.983\)     A1     N2

[3 marks]

Part (a) was handled well by most students.

Although this question was a rather straightforward question on binomial distribution, parts (b) and(c) seemed to cause much difficulty.

Although this question was a rather straightforward question on binomial distribution, parts (b) and(c) seemed to cause much difficulty. In part (c), finding at least one defective switch, many forgot to take the complement.