Foundation November 2017 Paper 2 Q21
21
(a) Noah starts to draw a tree diagram showing the outcomes of throwing a six when a fair dice is thrown twice.
(i) Complete the tree diagram. [1]
(ii) What is the probability of throwing two sixes? [2]
(b) Cara throws the same dice three times.
Show that the probability that Cara does not throw a six until her third throw is \(\dfrac{25}{216}\). [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) Correct probabilities filled | 1 | First Throw \(\dfrac{5}{6}\), Second Throw \(\dfrac{1}{6}, \dfrac{5}{6}, \dfrac{1}{6}, \dfrac{5}{6}\) | Accept equivalent fractions |
| (ii) \(\dfrac{1}{36}\) oe | 2 | M1 for \(\dfrac{1}{6} \times \textit{their } \dfrac{1}{6}\) | FT their tree diagram |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \(\dfrac{5}{6} \times \dfrac{5}{6}\) | M1 | M1 may be implied by a product of three fractions where two of them are \(\dfrac{5}{6}\) | |
| \(\dfrac{5}{6} \times \dfrac{5}{6} \times \dfrac{1}{6} = \dfrac{25}{216}\) | A1 | If 0 scored SC1 for \(\textit{their } \dfrac{5}{6} \times \textit{their } \dfrac{5}{6} \times \dfrac{1}{6}\) | For A1 product must be in this order FT their tree diagram bottom branch |