## Question 3(i):

**Method 1:**

$P(RB) + P(BR) = \frac{4}{12} \times \frac{8}{11} + \frac{8}{12} \times \frac{4}{11}$ | M1 | Multiply 2 probs together and summing two 2-factor probs, unsimplified, condone replacement |

$P(\text{diff colours}) = \frac{64}{132} \left(\frac{16}{33}\right) (0.485)$ | A1 | Correct answer |

**Method 2:**

$1 - P(BB) - P(RR) = 1 - \frac{4}{12} \times \frac{3}{11} - \frac{8}{12} \times \frac{7}{11}$ | M1 | Multiply 2 probs together and subtracting two 2-factor probs from 1, unsimplified, condone replacement |

$P(\text{diff colours}) = \frac{64}{132} \left(\frac{16}{33}\right)$ | A1 | Correct answer |

**Method 3:**

$P(\text{diff colours}) = \frac{(^4C_1 \times ^8C_1)}{^{12}C_2}$ | M1 | Multiply 2 combs together and dividing by a combination |

$= \frac{16}{33}$ | A1 | Correct answer |

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## Question 3(ii):

| Number of red socks | 0 | 1 | 2 |
|---|---|---|---|
| Prob | $\frac{14}{33}$ | $\frac{16}{33}$ | $\frac{3}{33}$ |

| B1 | Prob distribution table drawn, top row correct, condone additional values with $p = 0$ stated |

| B1 | $P(0)$ or $P(2)$ correct to 3sf (need not be in table) |

| B1 | All probs correct to 3sf, condone $P(0)$ and $P(2)$ swapped if correct |

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## Question 3(iii):

$E(X) = 1 \times \frac{16}{33} + 2 \times \frac{3}{33} = \frac{16}{33} + \frac{6}{33} = \frac{22}{33} \left(\frac{2}{3}\right)$ | B1ft | ft their table if 0, 1, 2 only, $0 < p < 1$ |

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