1MA0 Higher November 2015 Paper 2 Q25
25 Nomusa has 30 sweets.
She has
18 fruit sweets
7 aniseed sweets
5 mint sweets
Nomusa is going to take at random two sweets.
Work out the probability that the two sweets will not be the same type of sweet.
You must show all your working. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(\tfrac{18}{30}\times\tfrac{12}{29}+\tfrac{7}{30}\times\tfrac{23}{29}+\tfrac{5}{30}\times\tfrac{25}{29}\) or \(1 - \left(\tfrac{18}{30}\times\tfrac{17}{29}+\tfrac{7}{30}\times\tfrac{6}{29}+\tfrac{5}{30}\times\tfrac{4}{29}\right)\) or \(\tfrac{18}{30}\times\tfrac{7}{29}+\tfrac{18}{30}\times\tfrac{5}{29}+\tfrac{7}{30}\times\tfrac{18}{29}\) \(+\tfrac{7}{30}\times\tfrac{5}{29}+\tfrac{5}{30}\times\tfrac{18}{29}+\tfrac{5}{30}\times\tfrac{7}{29}\) | \(\dfrac{502}{870}\) | 4 | B1 for a second ‘branch’ probability seen (could be seen in a tree) M1 for a product of any first and second stage correct probabilities M1 for a complete method to find the required probability A1 for \(\tfrac{502}{870}\) oe Note if decimals used they must be correct to 2 decimal places SC with replacement B2 for \(\tfrac{502}{900}\) oe B0 M1 \(\tfrac{18}{30}\times\tfrac{12}{30}\) or \(\tfrac{7}{30}\times\tfrac{23}{30}\) or \(\tfrac{5}{30}\times\tfrac{25}{30}\) M1 \(\tfrac{18}{30}\times\tfrac{12}{30}+\tfrac{7}{30}\times\tfrac{23}{30}+\tfrac{5}{30}\times\tfrac{25}{30}\) A0 |