CAIE A-Level Mathematics Probability & Statistics 1 Question Bank

Includes all data
B1
Reference to either including all/raw data
or further statistical processes are possible that cannot be found using data from box-and-whisker, eg frequency, mean, mode or standard deviation not only median, IQR, range or spread which
can be found from both.

Key: 1|18| 2 means 181 cm for Amazons and 182 cm for Giants
B1
Correct stem can be upside down, ignore extra values
B1
Correct Amazons labelled on left, leaves in order from right to
left and lined up vertically (less than halfway to next column), no commas or other punctuation.
B1
Correct Giants labelled on same diagram, leaves in order and
lined up vertically (less than halfway to next column), no
commas or other punctuation.
B1
Correct single key for their diagram, need both teams identified and 'cm' stated at least once here or in leaf headings or title.
SC for if 2 separate diagrams drawn, award SCB1 if both keys meet these criteria (Max B1, B0, B0, B1)

$$\mathrm{UQ}=202\text{ cm},\qquad \mathrm{LQ}=182\text{ cm}, \qquad \mathrm{IQR}=202-182=20\text{ cm}.$$

$$\Sigma_{11}=2132,\qquad \Sigma_{15}=191.2(15)=2868.$$
Thus,
$$2868=2132+180+185+190+h, \qquad h=181\text{ cm}.$$

[8! =] 40320
B1
Evaluated, exact value only.

9!-2(8!)=362880-80640=282240.

${ }^{9} \mathrm{C}_{5}\left[\times{ }^{4} \mathrm{C}_{4}\right]$
M1
${ }^{9} \mathrm{C}_{x}\left[\times^{9-x} \mathrm{C}_{9-x}\right] x=4$, 5. Condone $\times 1$ for ${ }^{9-x} \mathrm{C}_{9-x}$.
Condone use of P .
126
A1
WWW

[Number of ways with Raman and Sanjay together on back row = ] $^{7} \mathrm{C}_{3}$
[Number of ways with Raman and Sanjay together on front row = ] $^{7} \mathrm{C}_{2}$
M1
${ }^{7} \mathrm{C}_{x}$ seen, x=3 or 2.
[Total =] 35+21
M1
Summing two correct scenarios.
56
A1
Evaluated - may be seen used in probability.
If M0 scored, SC B1 for 56 WWW.
Probability $=\frac{\text { their } 56}{\text { their }(c)}=\frac{56}{126}, \frac{4}{9}, 0.444$
B1 FT
FT their 56 from adding 2 or more scenarios in numerator and their (c) or correct as denominator.

The first success is on throw 3, 4, or 5:
$$\left(\frac13\right)\left(\frac23\right)^2+ \left(\frac13\right)\left(\frac23\right)^3+ \left(\frac13\right)\left(\frac23\right)^4.$$
M1

$$=\frac4{27}+\frac8{81}+\frac{16}{243}.$$
A1

$$=\frac{76}{243}=0.313\ldots$$
A1

$$E(X)=0\left(\frac8{27}\right)+1\left(\frac{12}{27}\right)+2\left(\frac6{27}\right)+3\left(\frac1{27}\right).$$
M1

$$E(X)=\frac{12}{27}+\frac{12}{27}+\frac3{27}=1.$$
A1