June 2024 Paper 2 Q6
6 The probability distribution of the discrete random variable \(X\) is shown in the table.
| \(x\) | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| \(\mathrm{P}(X = x)\) | 0.2 | \(a\) | \(3a\) | 0.4 |
(a) Calculate the value of the constant \(a\). [1]
(b) A single value of \(X\) is chosen at random.
Find the probability that the value is an odd number. [1]
Find the probability that the value is an odd number. [1]
(c) Two independent values of \(X\) are chosen at random.
Calculate the probability that the total of the two values is 3. [3]
Calculate the probability that the total of the two values is 3. [3]
| Scheme | Marks | AO |
|---|---|---|
| \([a =]\ 0.1\) | B1 | 1.1 |
| [1] |
| Scheme | Marks | AO |
|---|---|---|
| 0.5 | B1FT | 1.1 |
| [1] |
Notes
B1FT: FT their \(0.1 + 0.4\); \(0 \lt\) their \(a \lt\) their \(3a \lt 1\)
| Scheme | Marks | AO |
|---|---|---|
| \(0.2 \times 0.4\) oe or their \(3a \times\) their \(a\) oe seen | B1 | 1.1 |
| \(2 \times (0.2 \times 0.4 +\) their \(3a \times\) their \(a)\) | M1 | 3.1a |
| 0.22 | A1 | 1.1 |
| [3] |
Notes
B1: \(0.2 \times 0.4\) or \(0.3 \times 0.1\)
M1: NB \(2 \times (0.2 \times 0.4 + 0.3 \times 0.1)\); allow omission of 2; may be implied by 0.11