Higher June 2024 Paper 3 Q12
12 Cards are either gold or not gold.
P(gold) \(=\) 0.05
Harim chooses a card at random and replaces it.
He then chooses a second card.
(a) Complete the tree diagram. [2 marks]
(b) What is the probability that at least one of Harim’s cards is gold? [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Fully correct diagram | B2 | oe B1 0.95 seen once in correct position |
Additional guidance
| Answer | Mark | Comments |
|---|---|---|
| \(0.05 \times 0.05\) or 0.0025 or \(0.05 \times 0.95\) or \(0.95 \times 0.05\) or 0.0475 or \(0.95 \times 0.95\) or 0.9025 | M1 | oe ft their tree diagram in (a) if all probabilities are between 0 and 1 |
| \(1 - 0.95 \times 0.95\) or \(1 - 0.9025\) or \(0.05 \times 0.05 + 2 \times 0.05 \times 0.95\) or \(0.0025 + 2 \times 0.0475\) or \(0.0025 + 0.095\) | M1dep | oe ft their tree diagram in (a) if all probabilities are between 0 and 1 |
| 0.0975 or 0.098 | A1ft | oe eg \(\dfrac{39}{400}\) or 9.75% |
Additional guidance
Calculations or probabilities for part (b) may be seen on diagram in part (a)
If part (a) is incorrect full marks may be scored in part (b)