Foundation November 2024 Paper 1 Q19
19 The table shows the probabilities that a biased dice will land on 3, on 4, on 5 and on 6
| Number on dice | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Probability | 0.10 | 0.30 | 0.05 | 0.25 |
Karim assumes that the probabilities that the dice will land on 1 and on 2 are the same.
Karim rolls the biased dice 500 times.
(a) Assuming Karim is right, work out an estimate for the number of times the dice will land on 2 (3)
Karim is wrong.
The probability that the dice will land on 2 is greater than the probability that the dice will land on 1
(b) How does this information affect your answer to part (a)? (1)
| Answer | Mark | Mark scheme |
|---|---|---|
| 75 | P1 | for process to find sum of unknown probabilities eg \(1 - (0.10 + 0.30 + 0.05 + 0.25)\ (= 0.3)\) oe or for process to find number of times dice lands on 3, 4, 5 or 6 eg \((0.10 + 0.30 + 0.05 + 0.25) \times 500\ (= 350)\) oe |
| P1 | for a complete process, eg \((\text{``}0.3\text{''} \div 2) \times 500\) oe or \((500 - \text{``}350\text{''}) \div 2\) oe | |
| A1 | cao |
Additional guidance
Award mark for any two probabilities that sum to 0.3 eg in the table
or probability of 2 = 0.15
P1P1A0 for answer of 75:500 or \(\dfrac{75}{500}\)
| Answer | Mark | Mark scheme |
|---|---|---|
| Answer to part (a) will be greater | C1 | for an explanation that the answer will be greater Acceptable examples It makes the answer an underestimate The number will be higher The answer will increase / will go up The number of 2’s will increase It would be more than [75] Not acceptable examples My answer will change My answer is incorrect The calculation will change The probability will change It would make the probability of 2 go up My answer won’t change |
Additional guidance
Where [75] is their answer to (a)