Higher June 2018 Paper 3 Q6
6 There are some counters in a bag.
The counters are red or white or blue or yellow.
Bob is going to take at random a counter from the bag.
The table shows each of the probabilities that the counter will be blue or will be yellow.
| Colour | red | white | blue | yellow |
|---|---|---|---|---|
| Probability | 0.45 | 0.25 |
There are 18 blue counters in the bag.
The probability that the counter Bob takes will be red is twice the probability that the counter will be white.
A marble is going to be taken at random from a box of marbles.
The probability that the marble will be silver is 0.5
There must be an even number of marbles in the box.
| Answer | Mark | Mark scheme |
|---|---|---|
| 8 | P1 | for process to find sum of unknown probabilities, eg \(1 - 0.45 - 0.25\ (= 0.3)\) OR to find the total number of counters in the bag, eg \(\dfrac{18}{0.45}\ (= 40)\) OR to find the number of yellow counters, eg \(\dfrac{0.25}{0.45} \times 18\ (= 10)\) |
| P1 | for process to find P(red) = 0.2 oe or P(white) = 0.1 oe OR for process to find the total number of red and white counters, eg \(\text{``}40\text{''} - 18 - \text{``}10\text{''}\ (=12)\) OR for process to derive an equation in \(x\), eg \(2x + x = 1 - 0.45 - 0.25\) or \(2x + x = \text{``}0.3\text{''}\) or \(x = 0.1\) | |
| P1 | for a complete process to find the number of red counters, eg \(\dfrac{2 \times 0.1}{0.45} \times 18\) or \(\dfrac{2}{3} \times \text{``}12\text{''}\) or \(0.2 \times \text{``}40\text{''}\) or \(\dfrac{0.2}{0.025}\) | |
| A1 | cao |
Additional guidance
Award mark for any two probabilities given that sum to 0.3 eg given in the table.
Award P2 for P(red) or P(white) (could be shown in table)
Equations could be given as written statements or working but must be fully equivalent.
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanation | C1 | for explanation eg 0.5 multiplied by an odd number will never be a whole number, for half of a number to be an integer that number must be even, you can’t have half a marble |