Higher January 2020 Paper 2R Q16
16 Cody has two bags of counters, bag A and bag B.
Each of the counters has either an odd number or an even number written on it.
There are 10 counters in bag A and 7 of these counters have an odd number written on them.
There are 12 counters in bag B and 7 of these counters have an odd number written on them.
Cody is going to take at random a counter from bag A and a counter from bag B.
Harriet also has a bag of counters.
Each of her counters also has either an odd number or an even number written on it.
Harriet is going to take at random a counter from her bag of counters.
The probability that the number on each of Cody’s two counters and the number on Harriet’s counter will all be even is \(\dfrac{3}{100}\)
Show your working clearly. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{3}{10}\), \(\dfrac{7}{12}\), \(\dfrac{5}{12}\), \(\dfrac{7}{12}\), \(\dfrac{5}{12}\) | B2 |
| (2) |
Notes
| Scheme | Marks |
|---|---|
| \(\dfrac{7}{10} \times \text{“}\dfrac{5}{12}\text{”}\) or \(\text{“}\dfrac{3}{10}\text{”} \times \text{“}\dfrac{7}{12}\text{”}\) oe | M1ft |
| \(\dfrac{7}{10} \times \text{“}\dfrac{5}{12}\text{”} + \text{“}\dfrac{3}{10}\text{”} \times \text{“}\dfrac{7}{12}\text{”}\) oe | M1ft |
| \(\dfrac{56}{120}\) oe | A1 |
| (3) |
Notes
A1: eg \(\dfrac{7}{15}\) or 0.46… (2 dp truncated or rounded)
| Scheme | Marks |
|---|---|
| \(\text{“}\dfrac{3}{10}\text{”} \times \text{“}\dfrac{5}{12}\text{”} \times x = \dfrac{3}{100}\) oe | M1ft |
| \(x = \dfrac{3}{100} \div \text{“}\dfrac{15}{120}\text{”}\;\left(= \dfrac{6}{25}\right)\) oe | M1ft |
| Working required Answer: 25 | A1 |
| (3) | |
| (8 marks) |
Notes
M1ft: A correct equation involving the unknown probability
M1ft: Isolating or calculating the value of \(x\)
A1: Dep on M1