| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2020 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Probability of range of values |
| Difficulty | Moderate -0.8 Part (a) is a straightforward single probability calculation (0.22³). Part (b) requires computing P(2≤X≤4) = P(X=2) + P(X=3) + P(X=4) using the binomial formula with n=16, p=0.22, which is routine calculator work with no conceptual challenges. This is easier than average A-level, being a standard textbook exercise in applying the binomial distribution formula. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(0.22^3 = 0.0106\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(P(2,3,4) = \binom{16}{2}0.22^2 0.78^{14} + \binom{16}{3}0.22^3 0.78^{13} + \binom{16}{4}0.22^4 0.78^{12}\) | M1 | |
| \(0.179205 + 0.235877 + 0.216221\) | A1 | |
| \(0.631\) | A1 |
## Question 2:
### Part (a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $0.22^3 = 0.0106$ | B1 | |
### Part (b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $P(2,3,4) = \binom{16}{2}0.22^2 0.78^{14} + \binom{16}{3}0.22^3 0.78^{13} + \binom{16}{4}0.22^4 0.78^{12}$ | M1 | |
| $0.179205 + 0.235877 + 0.216221$ | A1 | |
| $0.631$ | A1 | |
---2 In a certain large college, $22 \%$ of students own a car.
\begin{enumerate}[label=(\alph*)]
\item 3 students from the college are chosen at random. Find the probability that all 3 students own a car.
\item 16 students from the college are chosen at random. Find the probability that the number of these students who own a car is at least 2 and at most 4 .
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2020 Q2 [4]}}