Higher November 2017 Paper 2 Q21
21 There are 12 counters in a bag.
There is an equal number of red counters, blue counters and yellow counters in the bag.
There are no other counters in the bag.
3 counters are taken at random from the bag.
(a) Work out the probability of taking 3 red counters. (2)
The 3 counters are put back into the bag.
Some more counters are now put into the bag.
There is still an equal number of red counters, blue counters and yellow counters in the bag.
There are no counters of any other colour in the bag.
3 counters are taken at random from the bag.
(b) Is it now less likely or equally likely or more likely that the 3 counters will be red?
You must show how you get your answer. (2)
You must show how you get your answer. (2)
| Answer | Mark | Notes |
|---|---|---|
| \(\dfrac{1}{55}\) | M1 | for \(\dfrac{4}{12} \times \dfrac{3}{11} \times \dfrac{2}{10}\) |
| A1 | for \(\dfrac{1}{55}\) oe |
| Answer | Mark | Notes |
|---|---|---|
| Conclusion (supported) | C1 | starts correct argument, eg by calculating a relevant probability, eg \(\dfrac{5}{15} \times \dfrac{4}{14} \times \dfrac{3}{13}\) |
| C1 | statement of “more likely” from eg comparison of probabilities, ft answer to (a) eg \(\dfrac{1}{55}\ (= 0.018\ldots)\) and \(\dfrac{2}{91}\ (= 0.021\ldots\) or \(0.022)\) |