## Question 5(i):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Tree diagram: first branches $\frac{6}{7}$ (T) and $\frac{1}{7}$ (C), second branches from T: $\frac{5}{9}$ (T), $\frac{4}{9}$ (C); from C: $\frac{6}{9}$ (T), $\frac{3}{9}$ (C) | B1 | First pair of branches labels and probs correct ($\frac{6}{7}$ and $\frac{1}{7}$ or rounding to 0.857 and 0.143). Labelling must be logically e.g. (T and T) or (T and Not T) acceptable |
| | B1 | Either of second top pair or bottom pair of branches labels and probs correct |
| | B1 | Both second pairs of branches labels and probs correct. No additional/further branches |

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## Question 5(ii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $T=0$: $\frac{3}{63}$ (0.0476(2)), $T=1$: $\frac{30}{63}$ (0.476(2)), $T=2$: $\frac{30}{63}$ (0.476(2)) | B1 | $P(1)$ correct |
| | B1 | $P(0)$ or $P(2)$ correct |
| | B1 | FT Correct values in table; any additional values of $T$ have stated probability of zero. For FT $\Sigma p = 1$ |

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## Question 5(iii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $E(X) = \frac{90}{63}\ \left(\frac{10}{7}\right)\ (1.43)$ | B1 | Not FT |

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## Question 5(iv):

| Answer | Marks | Guidance |
|--------|-------|----------|
| $P(1^\text{st}\ C \mid 2^\text{nd}\ T) = \frac{P(C\cap T)}{P(T)} = \frac{\frac{1}{7}\times\frac{6}{9}}{\frac{1}{7}\times\frac{6}{9}+\frac{6}{7}\times\frac{5}{9}} = \frac{\frac{6}{63}}{\frac{36}{63}}$ | B1 | $P(C\cap T)$ attempt seen as numerator of a fraction, consistent with $their$ tree diagram or correct |
| | M1 | Summing 2 appropriate two-factor probabilities, consistent with $their$ tree diagram or correct seen anywhere |
| | A1 | $\frac{36}{63}$ oe or correct unsimplified expression seen as numerator or denominator of a fraction |
| $\frac{1}{6}$ oe | A1 | Final answer |