Find the probability that a randomly chosen glass sheet contains at least one flaw.

Find the expected profit, $P$ dollars, per glass sheet.

Find the probability that it contains no flaws.

${\text{X}} \sim {\text{Po}}(0.5)$    (A1)

${\text{P}}(X \geqslant 1) = 0.393{\text{ }}( = 1 - {{\text{e}}^{ - 0.5}})$    (M1)A1

[3 marks]

${\text{P}}(X = 0) = 0.607 \ldots$    (A1)

${\text{E}}(P) = (0.607 \ldots  \times 5) - (0.393 \ldots  \times 3)$    (M1)

the expected profit is $1.85 per glass sheet     A1

[3 marks]

$Y \sim {\text{Po}}(2)$    (M1)

${\text{P}}(Y = 0) = 0.135{\text{ }}( = {{\text{e}}^{ - 2}})$    A1

[2 marks]

Part (a) was reasonably well done. Some candidates calculated ${\text{P}}(X = 1)$.

Part (b) was not as well done as expected with a surprising number of candidates calculating $5{\text{P}}(X = 0) + 3{\text{P}}(X \geqslant 1)$ rather than $5{\text{P}}(X = 0) - 3{\text{P}}(X \geqslant 1)$.

Part (c) was very well done.