Maryam has 7 sweets in a tin; 6 are toffees and 1 is a chocolate. She chooses one sweet at random and takes it out. Her friend adds 3 chocolates to the tin. Then Maryam takes another sweet at random out of the tin.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [B1] First pair of branches labels and probs correct (6/7 and 1/7 or rounding to 0.857 and 0.143) (for part (i))
2. [B1] Either of second top pair or bottom of branches labels and probs correct (for part (i))
3. [B1] Both second pairs of branches labels and probs correct. No additional / further branches. (for part (i))
4. [B1] P(1) correct (for part (ii))
5. [B1] P(0) or P(2) correct (for part (ii))
6. [B1 FT] Correct values in table, any additional values of T have stated probability of zero. For FT Σp = 1, (for part (ii))
7. [B1] Not FT (for part (iii))
8. [B1] P(C∩T) attempt seen as numerator of a fraction, consistent with their tree diagram or correct (for part (iv))
9. [M1] Summing 2 appropriate two-factor probabilities, consistent with their tree diagram or correct seen anywhere (for part (iv))
10. [A1] 36/63 oe or correct unsimplifed expression seen as numerator or denominator of a fraction (for part (iv))
11. [A1] Final answer (for part (iv))