17M.1.SL.TZ2.T_10

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The Home Shine factory produces light bulbs, 7% of which are found to be defective.

Francesco buys two light bulbs produced by Home Shine.

The Bright Light factory also produces light bulbs. The probability that a light bulb produced by Bright Light is not defective is $a$ .

Deborah buys three light bulbs produced by Bright Light.

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

[1]

Find the probability that both light bulbs are not defective.

[2]

b.i.

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

[2]

b.ii.

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

[1]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

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]

b.i.

$1 - 0.8649$ (M1)

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

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

Note: Follow through from part (a).

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

[2 marks]

b.ii.

$1 - {a^3}$ (A1) (C1)

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

[1 mark]

Examiners’ report

[N/A]

b.i.

[N/A]

b.ii.

[N/A]