Foundation June 2019 Unit 1 Q10
10. Twenty-five balls have numbers printed on them.
Some of the balls are coloured yellow (Y), the others are coloured blue (B).
The list below shows both the colour of each ball and the number printed on it.
| Y 76 | Y 217 | B 54 | B 126 | Y 21 |
| Y 438 | Y 32 | B 561 | B 194 | Y 69 |
| B 37 | B 518 | Y 94 | Y 157 | Y 208 |
| Y 382 | B 56 | B 234 | Y 72 | B 84 |
| Y 68 | Y 271 | Y 53 | B 100 | Y 321 |
(a) Complete the frequency table. [2]
| Type of ball | Yellow | Blue | ||
|---|---|---|---|---|
| Number \(\lt\) 100 | Number \(\geqslant\) 100 | Number \(\lt\) 100 | Number \(\geqslant\) 100 | |
| Frequency | 8 | |||
(b) How can you use your table to check that all the balls have been counted? [1]
(c) The 25 balls are placed in a box.
One ball is chosen at random.
What is the probability that it is a yellow ball numbered less than 100? [2]
One ball is chosen at random.
What is the probability that it is a yellow ball numbered less than 100? [2]
| Scheme | Marks | Comments | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| B2 | For all three correct. B1 for 1 or 2 correct. If no marks awarded allow B1 for all correct tallies seen. | ||||||||||||||
| Scheme | Marks | Comments |
|---|---|---|
| Any valid statement that indicates that the numbers (in the table) are added (to make 25) e.g. ‘add the frequency’. | E1 | Allow ‘add them up’. Allow sight of ‘8 + 7 + 4 + 6 (= 25).’ |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{8}{25}\) or equivalent ISW | B2 | B1 for x/25 with x<25. B1 for 8/y with y >8. Penalise incorrect notation -1; e.g. ‘8 out of 25’, 8:25, ‘8 in 25’. |