Higher June 2024 Paper 2 Q4
4 There are only red discs, blue discs and yellow discs in a bag.
There are 24 yellow discs in the bag.
Mel is going to take at random a disc from the bag.
The probability that the disc will be yellow is 0.16
the number of red discs : the number of blue discs = 5 : 4
Work out the number of red discs in the bag. (4)
| Answer | Mark | Mark scheme |
|---|---|---|
| 70 | P1 | for process to find number of discs in the bag, eg \(24 \div 0.16\ (= 150)\) or for process to find the total probability of red or blue, eg \(1 - 0.16\ \left(= 0.84 \text{ or } \dfrac{21}{25} \text{ oe}\right)\) |
| P1 | for process to work with the ratio eg \(([\text{total}] - 24) \div (5 + 4)\ (= 14)\) or for a process to find the probability of red, eg \([\text{probability}] \div (5 + 4) \times 5\ \left(= 0.46\ldots \text{ or } \dfrac{7}{15}\right)\) | |
| P1 | for a complete correct process to find the number of red discs eg \(\text{``}14\text{''} \times 5\) or \(\text{``}0.46\ldots\text{''} \times 24 \div 0.16\) or an answer of \(\dfrac{70}{150}\) | |
| A1 | for 70 |
Additional guidance
May be implied by 126
0.46 or better or 0.47 may imply P2
[total] can be any integer
[probability] can be any value less than 1
If correct processes seen to find the total for both red and blue or 70 : 56 award P3
Must come from correct use of probability and ratio in either order
If the values for red and blue are found, the value for red must be clearly identified as the answer to gain A1