| Date | May 2017 | Marks available | 2 | Reference code | 17M.1.sl.TZ2.10 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 10 | Adapted from | N/A |
Question
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.
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.
Markscheme
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]
