| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Basic two-way table probability |
| Difficulty | Easy -1.8 This is a straightforward two-way table question requiring only basic probability calculations: reading values from a table, simple division for probabilities, and conditional probability using the definition P(A|B) = P(A∩B)/P(B). Part (iii) tests understanding of mutually exclusive events through direct observation of the table. Part (iv) involves a simple product of two independent selections. No problem-solving insight or complex reasoning required—purely mechanical application of basic S1 formulas. |
| Spec | 2.03a Mutually exclusive and independent events2.03d Calculate conditional probability: from first principles |
| Birth rate | ||||
| \cline { 3 - 5 } \multicolumn{2}{|c|}{} | Low | Medium | High | |
| \multirow{3}{*}{GDP} | Low | 3 | 5 | 45 |
| \cline { 2 - 5 } | Medium | 20 | 42 | 12 |
| \cline { 2 - 5 } | High | 35 | 8 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \([0 = 8^2 - 2gs]\) | M1 | For using \(0 = u^2 - 2gs\) |
| Maximum height is 3.2 m | A1 | |
| \([v^2 = 8^2 - 2g \times 1.6]\) | M1 | For using \(v^2 = u^2 - 2gs\) |
| Speed is 5.66 ms\(^{-1}\) | A1 | 4 marks total |
| (ii) \([5.65685... = 8 - 10t]\) | M1 | For using \(v = u - gt\) |
| Time is 0.234 s | A1 | 2 marks total |
**(i)** $[0 = 8^2 - 2gs]$ | M1 | For using $0 = u^2 - 2gs$
Maximum height is 3.2 m | A1 |
$[v^2 = 8^2 - 2g \times 1.6]$ | M1 | For using $v^2 = u^2 - 2gs$
Speed is 5.66 ms$^{-1}$ | A1 | 4 marks total
**(ii)** $[5.65685... = 8 - 10t]$ | M1 | For using $v = u - gt$
Time is 0.234 s | A1 | 2 marks total
---3 Ronnie obtained data about the gross domestic product (GDP) and the birth rate for 170 countries. He classified each GDP and each birth rate as either 'low', 'medium' or 'high'. The table shows the number of countries in each category.
\begin{center}
\begin{tabular}{ | c | l | c | c | c | }
\hline
\multicolumn{2}{|c|}{} & \multicolumn{3}{|c|}{Birth rate} \\
\cline { 3 - 5 }
\multicolumn{2}{|c|}{} & Low & Medium & High \\
\hline
\multirow{3}{*}{GDP} & Low & 3 & 5 & 45 \\
\cline { 2 - 5 }
& Medium & 20 & 42 & 12 \\
\cline { 2 - 5 }
& High & 35 & 8 & 0 \\
\hline
\end{tabular}
\end{center}
One of these countries is chosen at random.\\
(i) Find the probability that the country chosen has a medium GDP.\\
(ii) Find the probability that the country chosen has a low birth rate, given that it does not have a medium GDP.\\
(iii) State with a reason whether or not the events 'the country chosen has a high GDP' and 'the country chosen has a high birth rate' are exclusive.
One country is chosen at random from those countries which have a medium GDP and then a different country is chosen at random from those which have a medium birth rate.\\
(iv) Find the probability that both countries chosen have a medium GDP and a medium birth rate.
\hfill \mbox{\textit{CAIE S1 2012 Q3 [8]}}