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Date May 2017 Marks available 2 Reference code 17M.1.SL.TZ2.T_10
Level Standard Level Paper Paper 1 Time zone Time zone 2
Command term Find Question number T_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.

[1]
a.

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]
c.

Markscheme

* 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]

a.

0.93 × 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   ( unless it follows  93 100 × 92 99 ) .

 

[2 marks]

b.i.

1 0.8649     (M1)

 

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

 

OR

0.07 × 0.07 + 2 × ( 0.07 × 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 ) + 3 a ( 1 a ) 2 + ( 1 a ) 3 or equivalent.

 

[1 mark]

c.

Examiners report

[N/A]
a.
[N/A]
b.i.
[N/A]
b.ii.
[N/A]
c.

Syllabus sections

Topic 4—Statistics and probability » SL 4.6—Combined, mutually exclusive, conditional, independence, prob diagrams
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Topic 4—Statistics and probability

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