Higher January 2020 Paper 2 Q14
14 There are 20 glasses in a cupboard.
13 of the glasses are large
7 of the glasses are small
Roberto takes at random two glasses from the cupboard.
(a) Complete the probability tree diagram. (2)
(b) Work out the probability that Roberto takes two small glasses. (2)
| Scheme | Marks |
|---|---|
| B1 | |
| Correct probabilities on the tree diagram | B1 |
| (2) |
Notes
B1: for \(\dfrac{13}{20}\) and \(\dfrac{7}{20}\) on the first branch (0.65 and 0.35)
B1: for \(\dfrac{12}{19}\), \(\dfrac{7}{19}\), \(\dfrac{13}{19}\) and \(\dfrac{6}{19}\) on the second branch
(accept 2 dp or better 0.6315..., 0.3684..., 0.6842..., 0.3157...)
| Scheme | Marks |
|---|---|
| \(\dfrac{7}{20} \times \dfrac{6}{19}\) oe only | M1 |
\(\dfrac{21}{190}\) Answer: \(\dfrac{21}{190}\) | A1 |
| (2) | |
| (4 marks) |
Notes
M1: ft from (a) as long as probabilities less than 1
A1: for \(\dfrac{21}{190}\) oe or 0.11… (at least 2 dp)