# Question 6:

## Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| 0.16 oe | B1 | Correct probability |

## Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[P(C)=] 0.04+0.15+0.12+p [=0.31+p]$; $[P(S)=] 0.1+0.15+0.12+0.23[=0.6]$; $[P(S \cap C)=] 0.15+0.12[=0.27]$ | M1 | For 2 correct probability expressions |
| All three expressions correct; $[P(C')=] 0.1+0.23+q[=0.33+q]$; $[P(S')=]0.4$; $[P(S'\cap C')=]q$ | M1 | All 3 correct probability expressions; allow $P(C)=0.45$ |
| $(\text{"0.31"}+p)\times\text{"0.6"} = \text{"0.27"}$ oe; or $(\text{"0.33"}+q)\times\text{"0.4"} = q$ oe | M1d | Dependent on 1st M1; for use of $P(C\cap S)=P(C)\times P(S)$ or $P(C'\cap S')=P(C')\times P(S')$ ft their probabilities if labelled clearly |
| $p = 0.14$ oe; $q = 0.22$ oe | A1 | For 0.14 or exact equivalent or 0.22 or exact equivalent |

## Part (c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $q = 1-(0.04+0.12+0.15+0.1+0.23+\text{"p"})$; or $p = 1-(0.04+0.12+0.15+0.1+0.23+\text{"q"})$ | M1 | For correct expression for $q$ ft their $p$ or correct expression for $p$ ft their $q$ |
| $q = 0.22$ oe; $p = 0.14$ oe | A1ft | For 0.22 or exact equivalent ft their $p$, or 0.14 or exact equivalent ft their $q$ ($p+q=0.36$ provided $p$ and $q$ are probabilities) |

## Part (d)(i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[P((C \cup S) \cap G')] = 0.39$ oe | B1 | For 0.39 or exact equivalent; do not allow $0.04+0.12+0.23$ |

## Part (d)(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $P(C \mid (S \cap G)) = \frac{0.15}{0.15+0.1}$ | M1 | For $\frac{0.15}{0.15+0.1}$ |
| $= 0.6$ oe | A1 | For 0.6 or exact equivalent |

## Part (e):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Number of teenagers $= \frac{76}{0.15+\text{"p"}}$ oe | M1 | Relating 76 to their $P(C \cap G)$; may be implied by awrt 262 |
| Number who don't play Scrabble $= \text{"}\!\left(\frac{76}{0.15+p}\right)\!\text{"} \times 0.4\ (= 104.8\ldots)$ | M1 | For number of teenagers $\times 0.4$ ft their number of teenagers e.g. $0.4 \times \text{"262"}$; provided number of teenagers is not 76 |
| $= 104.8\ldots$ awrt 105 | A1 | awrt 105 ISW |

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