| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2012 |
| Session | June |
| Marks | 5 |
| Topic | Normal Distribution |
| Type | Single tail probability P(X < a) or P(X > a) |
| Difficulty | Moderate -0.8 This is a straightforward geometric distribution question requiring only recognition of the distribution and direct application of the formula P(X=n) = (1-p)^(n-1) × p. The calculations involve simple arithmetic with p=1/5, making this easier than average A-level work despite being from Pre-U. |
| Spec | 5.02f Geometric distribution: conditions5.02g Geometric probabilities: P(X=r) = p(1-p)^(r-1) |
State Geometric — B1 [1]
**(ii)** Attempt $\left(\frac{4}{5}\right)^2\left(\frac{1}{5}\right)$ — M1
Obtain $\frac{16}{125} = 0.128$ — A1 [2]
**(iii)** Attempt $\frac{1}{5} + \left(\frac{4}{5}\right)\left(\frac{1}{5}\right)$ — M1
Or $1 - \left(\frac{4}{5}\right)^2$
Obtain $\frac{9}{25} = 0.36$ — A1 [2]
**Total: [5]**
*SC When $p = \frac{1}{4}$ used, allow max M1A0 for both (ii) and (iii).*2 A bag contains four black balls and one white ball. A man chooses a ball at random. If it is a black ball, he replaces it and chooses another at random. If he chooses the white ball, he stops.\\
(i) Name the probability distribution which models this situation.\\
(ii) Calculate the probability that he will make exactly three attempts before he stops.\\
(iii) Calculate the probability that he will make fewer than three attempts before he stops.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2012 Q2 [5]}}