Higher June 2018 Paper 5 Q8
8 Hannah wants to display all the possible outcomes when rolling two fair 6-sided dice.
(a) Give a reason why a tree diagram is not the best method to use. [1]
(b)
(i) Draw a sample space to display all the possible outcomes. [2]
(ii) Show that the probability of the scores on the two dice adding to 11 is \(\dfrac{1}{18}\). [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Too many branches oe | 1 | Accept e.g. Takes too long oe Tree would be too big oe Too complicated oe Too hard to draw oe Tree diagrams are better for fewer outcomes oe Do not accept e.g. Trees can only have two branches | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) Attempts sample space | M1 | Presented in any clear form, including list or table | For M1, accept two by two table drawn with row and column labelled 1 to 6 [with no entries or with incorrect entries] For M1 accept as a list of at least 6 different pairs or totals |
| 36 correct outcomes | A1 | Pairs shown or accept as totals in table | with no others or no repeats If listing as pairs on table, condone e.g. (2, 1) listed as (1, 2) etc |
| (ii) \(\dfrac{2}{36} = \dfrac{1}{18}\) | 2 | M1 for (5, 6) and (6, 5) identified or for \(2\left(\dfrac{1}{6} \times \dfrac{1}{6}\right)\) oe | Accept indicated on sample space |