| Part | Answer/Working | Marks | Guidance |
|------|---|---|---|
| (a) | Tree diagram with: Age branch ($p$, $< 50$ and $\geq 50$ condone $> 50$) and Computer use branch (0.80, 0.20 daily and not daily for $< 50$; 0.55, 0.45 daily and not daily for $\geq 50$) | B1, B1 | 1st B1 for correct shape (2 branches then 4 branches) and correct labels on first set of branches ($p$, $< 50$ and $\geq 50$ condone $> 50$). 2nd B1 for correct labels on second set of branches (0.80, 0.55, daily and not daily). Allow 0.8p and 0.55(1-p) on or at the end of the appropriate branches. NB they do not require the probabilities in brackets for either of these two marks. Allow labels U(use) and $U'$ or N and NE. Condone 80% and 55% etc on tree diagram and in (b). |
| | | (2) | |
| (b) | $p \times 0.80 + (1-p) \times 0.55 = 0.70$ | M1 | M1 for a correct equation to find $p$ using their tree diagram. |
| | | $p = 0.6$ | A1 | A1 for 0.6 [condone 60%] (Correct answer only will score M1A1) |
| | | (2) | |
| (c) | $[P(< 50 \mid \text{use computer daily}) =] \frac{P(< 50 \cap \text{use computer daily})}{P(\text{use computer daily})} = \frac{\text{'0.6'} \times 0.80}{0.70}$ | M1 | M1 for a correct expression with 0.70 substituted correctly and numerator $<$ denominator or correct ratio of probabilities f.t. their $p$ provided $0 < p < \frac{2}{3}$. |
| | | $= \frac{48}{70}$ | A1oe | A1oe for $\frac{48}{70}$ or an exact equivalent e.g. $\frac{24}{35}$ (Correct answer only is M1A1) |
| | | | Allow awrt 0.686 following a correct expression. [68.6% is A0] |
| | | (2) | |
| | | [6 marks] | |