## Question 6:

### Part (i):

| Answer/Working | Marks | Guidance |
|---|---|---|
| Table of $X$ values with Spinner A values 1, 2, 3, 3 and Spinner B values $-3, -2, -1, 1$: resulting in values $(-2), -1, 0, 0; -1, 0, (1), 1; 0, 1, 2, 2; 2, 3, 4, 4$ | B1 (1) | |

### Part (ii):

| Answer/Working | Marks | Guidance |
|---|---|---|
| $x$: $-2, -1, 0, 1, 2, 3, 4$ | M1 | Their values in (i) as the top line, seen listed in (ii) or used in part (iii) |
| prob: $\frac{1}{16}, \frac{2}{16}, \frac{4}{16}, \frac{3}{16}, \frac{3}{16}, \frac{1}{16}, \frac{2}{16}$ | M1 | Attempt at probs seen evaluated, need at least 4 correct from their table |
| | A1 (3) | Correct table seen |

### Part (iii):

| Answer/Working | Marks | Guidance |
|---|---|---|
| $E(X) = 1$ | M1 | Attempt at $E(X)$ from their table if $\Sigma p = 1$ |
| $\text{Var}(X) = ((-2)^2 + 2 + 3 + 12 + 9 + 32)/16 - 1^2$ | M1 | Evaluating $\Sigma x^2 p - [\text{their } E(X)]^2$, allow $\Sigma p \neq 1$ but all $p$'s $< 1$ |
| $= \frac{62}{16} - 1 = \frac{23}{8}\ (2.875)$ | A1 (3) | Correct answer |
| OR using $\Sigma p(x-\bar{x})^2 = (9+8+4+0+3+4+18)/16 = \frac{46}{16} = 2.875$ | M1, M1, A1 | |

### Part (iv):

| Answer/Working | Marks | Guidance |
|---|---|---|
| $P(\text{even given} +\text{ve}) = \frac{5}{9}$ | M1 | Counting their even numbers and dividing by their positive numbers |
| | A1 (2) | Correct answer |
| OR $P(\text{even given} +\text{ve}) = \dfrac{\left(\frac{5}{16}\right)}{\left(\frac{9}{16}\right)} = \frac{5}{9}$ | M1 | Using cond prob formula, not $P(E) \times P(+\text{ve})$, need fraction over fraction, accept any of $\frac{5/16\ \text{or}\ 6/16\ \text{or}\ 9/16}{9/16\ \text{or}\ 10/16\ \text{or}\ 13/16}$ |
| | A1 | Correct answer |

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