Page 92 - Math SL HB Sem 3

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[Maximum mark; l SJ '1lo' sP> 1 79

' or Frcnch' rt is known that75 %of the s,ra"*" r."-ip*ish, and 40 % learn French.
,$ Lt a large school, students are required to learn at least one language, Spanish

(a) Find the percentage ofstudents who leam both Spanish and French.
[2 marksJ

but not French,
(b) Find the percentage ofstudents who rearn
_Spanish, [2 mar*sJ

At this school, 52 % ofthe students arc girls, and g5 o/oof
the girls learn Spanish.
,.
(c) A student is chosen at random. Let G be the event that the student is a girl, and
let S be the event that the student leams Spanish.

(i) Find p(GaS).

(iD Show that G and S are not independent.
[5 marksJ
(d)
A boy is chosen at random. Find the probabiljty that he learns Spanish.
[6 mork.rJ

[Mcimwt mark: 7] tle<- Sl , TU
*
The probability of obtaining heads on a biased coin is 0.4. The coin is tossed
600 times.

(a) (i) Write down the mean number ofheads.

(ii) Find the standard deviation ofthe number ofheads. [4 marks]

(b) Find the probability that the number of heads obtained is less than one standard
deviation away from the mean. [3 narksJ

8]
$ [Maximummarh Nn- sYL [-tD

In a large city, the time taken to travel to work is normalty distributed with
*"* p Ld ,i-d*a deviation o . It is found that 4 yo of the population take less
than 5 minutes to gst to work, and 70 % take less than 25 minutes'

Find the value of P eind of o .

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