Write down the probability that a light bulb produced by Home Shine is not defective.

Find the probability that both light bulbs are not defective.

Find the probability that at least one of Francesco’s light bulbs is defective.

Write down an expression, in terms of $a$, for the probability that at least one of Deborah’s three light bulbs is defective.

0.93 (93%)     (A1)     (C1)

[1 mark]

$0.93 \times 0.93$     (M1)

Note:     Award (M1) for squaring their answer to part (a).

0.865 (0.8649; 86.5%)     (A1)(ft)     (C2)

Notes:     Follow through from part (a).

Accept $0.86{\text{ }}\left( {{\text{unless it follows }}\frac{{93}}{{100}} \times \frac{{92}}{{99}}} \right)$.

[2 marks]

$1 - 0.8649$     (M1)

Note:     Follow through from their answer to part (b)(i).

OR

$0.07 \times 0.07 + 2 \times (0.07 \times 0.93)$     (M1)

Note:     Follow through from part (a).

0.135 (0.1351; 13.5%)     (A1)(ft)     (C2)

[2 marks]

$1 - {a^3}$     (A1)     (C1)

Note:     Accept $3{a^2}(1 - a) + 3a{(1 - a)^2} + {(1 - a)^3}$ or equivalent.

[1 mark]