| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2018 |
| Session | June |
| Marks | 5 |
| Topic | Discrete Probability Distributions |
| Type | Construct probability distribution from scenario |
| Difficulty | Easy -1.2 This is a straightforward probability distribution question requiring basic coin probability calculations (each outcome has probability 1/4), constructing a simple table, computing expectation using the standard formula, and comparing E(X) to the cost. All steps are routine applications of standard techniques with no problem-solving insight required, making it easier than average. |
| Spec | 2.04a Discrete probability distributions5.02b Expectation and variance: discrete random variables |
| Answer | Marks | Guidance |
|---|---|---|
| \(x\) | \(0\) | \(20\) |
| \(P(X=x)\) | \(0.5\) | \(0.25\) |
**Question 3(i)**
| $x$ | $0$ | $20$ | $100$ |
|---|---|---|---|
| $P(X=x)$ | $0.5$ | $0.25$ | $0.25$ |
One correct pair **B1**
All correct **B1**
**Question 3(ii)**
Attempt at use of $E(X)$ formula **M1**
$0 \times 0.5 + 20 \times 0.25 + 100 \times 0.25 = 30$ **A1** Allow if £0.3(0); allow if tell us working in £
**Question 3(iii)**
$s > 30$ **B1** **FT** *their* **(ii)**3 John plays a game with two unbiased coins. John tosses the coins. If he gets two heads he wins $\pounds 1$. If he gets two tails he wins 20 p. If he gets one head and one tail he wins nothing. Let $X$ be the random variable for the amount of money, in pence, John wins per game.\\
(i) Construct a probability distribution table for $X$.\\
(ii) Calculate $\mathrm { E } ( X )$.\\
(iii) John pays $s$ pence to play the game. State the values of $s$ for which John should expect to make a loss.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2018 Q3 [5]}}