S2 January 2010 Q3

Notes

B1 for seeing or using Po(0.25)

M1 for finding \(\mathrm{P}(Y = 0)\) either by \(\mathrm{e}^{-a}\), where \(a\) is positive (\(a\) needn’t equal their \(\lambda\)) or using tables if their value of \(\lambda\) is in them
Beware common Binomial error using, \(p = 0.05\) gives 0.7738 but scores B0 M0 A0

A1 awrt 0.779

SC Use of Binomial. Mark parts a and b as scheme. They could get (a) B0,M0,A0 (b) B0 M1 A0

Notes

B1 for stating or a clear use of Po(0.4) in part (b) or (c)
M1 for writing or finding \(1 - \mathrm{P}(X = 0)\)
A1 awrt 0.33

SC Use of Binomial. Mark parts a and b as scheme. They could get (a) B0,M0,A0 (b) B0 M1 A0

Notes

M1 for finding \(\mathrm{P}(X = 2)\) e.g \(\dfrac{\mathrm{e}^{-\lambda}\lambda^2}{2!}\) with their value of \(\lambda\) in
or if their \(\lambda\) is in the table for writing \(\mathrm{P}(X \leqslant 2) - \mathrm{P}(X \leqslant 1)\)
A1 awrt 0.0536

SC Use of Binomial. In part c allow M1 for \({}^{n}C_2\,(p)^2(1 - p)^{n-2}\) with “their n” and “their \(p\)”. They could get (c) M1,A0
DO NOT GIVE for \(p(x \leqslant 2) - p(x \leqslant 1)\)

Notes

1st B1 their answer to part(b) correct to 2 sf or awrt 0.33
2nd B1 need the word independent. This is dependent on them gaining the first B1

SC Use of Binomial. In (d) they can get the first B1 only. They could get (d) B1B0