| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Conditional Probability |
| Type | Basic two-way table probability |
| Difficulty | Moderate -0.8 This is a straightforward S1 question involving basic two-way table construction and standard probability calculations (conditional probability, combinations). Part (a) requires organizing given information, parts (b) use simple probability formulas, and part (c) applies basic combinatorics with no conceptual challenges—all routine textbook exercises requiring minimal problem-solving. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space5.01a Permutations and combinations: evaluate probabilities |
| Answer | Marks |
|---|---|
| (a) Venn diagram with circles labeled "male" and "full-time", with 13 in left only, 26 in intersection, 21 in right only, and 15 outside both circles | B3 |
| (b)(i) \(\frac{26}{78} = \frac{1}{3}\) | M1 A1 |
| (b)(ii) \(\frac{13}{39} = \frac{1}{3}\) | M1 A1 |
| (c)(i) \(\frac{26}{78} \times \frac{26}{78} \times \frac{25}{77} = 0.240\) (3sf) | M2 A1 |
| (c)(ii) \(1 - P(\text{all male}) = 1 - (\frac{26}{78} \times \frac{26}{78} \times \frac{25}{77}) = 0.865\) (3sf) | M3 A1 |
| (14) |
**(a)** Venn diagram with circles labeled "male" and "full-time", with 13 in left only, 26 in intersection, 21 in right only, and 15 outside both circles | B3 |
**(b)(i)** $\frac{26}{78} = \frac{1}{3}$ | M1 A1 |
**(b)(ii)** $\frac{13}{39} = \frac{1}{3}$ | M1 A1 |
**(c)(i)** $\frac{26}{78} \times \frac{26}{78} \times \frac{25}{77} = 0.240$ (3sf) | M2 A1 |
**(c)(ii)** $1 - P(\text{all male}) = 1 - (\frac{26}{78} \times \frac{26}{78} \times \frac{25}{77}) = 0.865$ (3sf) | M3 A1 |
| | | (14) |
---5. A College employs 75 teachers, of whom 47 are full-time and the rest are part-time. Of the 39 male teachers at the College, 26 are full-time.
\begin{enumerate}[label=(\alph*)]
\item Represent this information on a Venn diagram.
\item One teacher is selected at random to be interviewed by an inspector. Find the probability that the teacher chosen
\begin{enumerate}[label=(\roman*)]
\item works full-time and is female,
\item works part-time, given that he is male.
\end{enumerate}\item Three teachers are selected at random to be observed by an inspector during one day. Find correct to 3 significant figures the probability that
\begin{enumerate}[label=(\roman*)]
\item all three teachers chosen work full-time,
\item at least one of the three teachers chosen is female.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [14]}}