| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Probability distribution table |
| Difficulty | Moderate -0.8 This is a straightforward binomial distribution question with n=5, p=1/4. Part (i) is a simple verification calculation using the binomial formula, and part (ii) requires computing P(X=r) for r=0 to 5 using the same formula repeatedly. It tests basic understanding of binomial probability with no problem-solving or conceptual challenges beyond routine application. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| For relevant binomial calculation, need \(_5C_4\) or 5 or all 5 options | M1 | |
| For correct answer. AG | A1 [2] | |
| (ii) | X | 0 |
| \(P(X = x)\) | 0.2373 | 0.3955 |
| Answer | Marks | Guidance |
| For all correct X values | B1 | |
| For one correct prob excluding \(P(X = 4)\) | B1 | |
| For 2 correct probs excluding \(P(X = 4)\) | B1 | |
| For 3 correct probs excluding \(P(X = 4)\) | B1 | |
| All correct and in decimals | B1 [5] | |
| (cont.) | X | 3 |
| \(P(X = x)\) | 0.0879 | 0.0146 |
(i) $P(G, G, G, G, NG) = (0.25)^4 \times (0.75)^1 \times {}_5C_4 = 0.0146$ AG
| Answer | Marks | Guidance |
|--------|-------|----------|
| For relevant binomial calculation, need $_5C_4$ or 5 or all 5 options | M1 | |
| For correct answer. AG | A1 [2] | |
(ii) | X | 0 | 1 | 2 |
| $P(X = x)$ | 0.2373 | 0.3955 | 0.2637 |
| Answer | Marks | Guidance |
|--------|-------|----------|
| For all correct X values | B1 | |
| For one correct prob excluding $P(X = 4)$ | B1 | |
| For 2 correct probs excluding $P(X = 4)$ | B1 | |
| For 3 correct probs excluding $P(X = 4)$ | B1 | |
| All correct and in decimals | B1 [5] | |
(cont.) | X | 3 | 4 | 5 |
| $P(X = x)$ | 0.0879 | 0.0146 | 0.0010 |
---3 A fair dice has four faces. One face is coloured pink, one is coloured orange, one is coloured green and one is coloured black. Five such dice are thrown and the number that fall on a green face are counted. The random variable $X$ is the number of dice that fall on a green face.\\
(i) Show that the probability of 4 dice landing on a green face is 0.0146 , correct to 4 decimal places.\\
(ii) Draw up a table for the probability distribution of $X$, giving your answers correct to 4 decimal places.
\hfill \mbox{\textit{CAIE S1 2005 Q3 [7]}}