Higher November 2020 Paper 3 Q22
22 Visitors to a museum buy a child ticket or an adult ticket.
Here is some information about two groups of visitors.
| Group X | 250 visitors, including 120 children |
|---|---|
| Group Y | number of children : number of adults = 17 : 15 |
One visitor from each group is picked at random.
Is this statement correct?
| Probability of picking two children > probability of picking two adults |
You must show your working. [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{120}{250}\) or 0.48 or \(\dfrac{130}{250}\) or 0.52 or \(\dfrac{17}{32}\) or 0.53125 or \(\dfrac{15}{32}\) or 0.46875 | M1 | oe |
| \(\dfrac{120}{250} \times \dfrac{17}{32}\) or \(\dfrac{51}{200}\) or 0.255 | M1 | oe implies 1st and 2nd M1 |
| \(\dfrac{130}{250} \times \dfrac{15}{32}\) or \(\dfrac{39}{160}\) or 0.24375 | M1 | oe implies 1st and 3rd M1 |
| 0.255 and 0.24375 and Yes | A1 | must be comparable if fractions used eg \(\dfrac{204}{800}\) and \(\dfrac{195}{800}\) and Yes |
Additional guidance
Accept values given as percentages
Accept decimal values truncated or rounded to 2 dp or better