| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Incomplete two-way table completion |
| Difficulty | Moderate -0.8 This is a straightforward two-way table completion requiring basic probability arithmetic (addition/subtraction of fractions) and one conditional probability calculation using P(A|B) = P(A∩B)/P(B). All values are given directly or follow immediately from row/column totals, requiring no problem-solving insight beyond applying standard formulas. |
| Spec | 2.03c Conditional probability: using diagrams/tables |
| Kitchen left in a mess | Kitchen not left in a mess | Total | |
| Meal served on time | \(\frac { 1 } { 5 }\) | ||
| Meal not served on time | \(\frac { 3 } { 10 }\) | ||
| Total | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Table: Kitchen mess/not mess rows; On time \(\frac{1}{10}\), \(\frac{1}{10}\); Not on time \(\frac{1}{2}\); Total \(\frac{4}{5}\), \(\frac{3}{5}\), \(\frac{4}{10}\) | B1 | 2 probabilities correct |
| B1 | 2 further probabilities correct | |
| B1 [3] | 2 further probabilities correct |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(P(\text{not on time given kitchen mess}) = \frac{1/2}{3/5}\) | M1 | A conditional prob fraction seen (using corresponding combined outcomes and total) |
| \(= \frac{5}{6}\) o.e. | A1 [2] | FT from their values, 3sf or better, \(<1\), \(\frac{3}{5}\text{ft}<1\) |
## Question 2:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Table: Kitchen mess/not mess rows; On time $\frac{1}{10}$, $\frac{1}{10}$; Not on time $\frac{1}{2}$; Total $\frac{4}{5}$, $\frac{3}{5}$, $\frac{4}{10}$ | B1 | 2 probabilities correct |
| | B1 | 2 further probabilities correct |
| | B1 **[3]** | 2 further probabilities correct |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $P(\text{not on time given kitchen mess}) = \frac{1/2}{3/5}$ | M1 | A conditional prob fraction seen (using corresponding combined outcomes and total) |
| $= \frac{5}{6}$ o.e. | A1 **[2]** | FT from their values, 3sf or better, $<1$, $\frac{3}{5}\text{ft}<1$ |
---2 When Joanna cooks, the probability that the meal is served on time is $\frac { 1 } { 5 }$. The probability that the kitchen is left in a mess is $\frac { 3 } { 5 }$. The probability that the meal is not served on time and the kitchen is not left in a mess is $\frac { 3 } { 10 }$. Some of this information is shown in the following table.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
& Kitchen left in a mess & Kitchen not left in a mess & Total \\
\hline
Meal served on time & & & $\frac { 1 } { 5 }$ \\
\hline
Meal not served on time & & $\frac { 3 } { 10 }$ & \\
\hline
Total & & & 1 \\
\hline
\end{tabular}
\end{center}
(i) Copy and complete the table.\\
(ii) Given that the kitchen is left in a mess, find the probability that the meal is not served on time.
\hfill \mbox{\textit{CAIE S1 2015 Q2 [5]}}