Jasmine has one $5 coin, two $2 coins and two $1 coins. She selects two of these coins at random. The random variable X is the total value, in dollars, of these two coins.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [B1] AG Must include [$7], 5, 2 and link the probabilities to the appropriate value ['C1 x 2C1 / 5C2] = 0.2. 1/5 x 2/4 = 1/2 x 1/2 unless 5 and 2 and 2 and 5 seen in solution. If all possibilities identified (e.g. outcome table), must be clearly labelled and terms fulfilling the condition identified.
2. [B1] Table with correct x values and at least one further non-zero probability correct. Condone extra x values if probability stated as 0.
3. [B1] Two more correct non-zero probabilities linked with correct outcomes. Accept probabilities not in table if clearly identified.
4. [B1] All five probabilities correct. Accept probabilities not in table if clearly identified. SC B1 for four further non-zero probabilities adding to 0.8 if B1 max scored.
5. [M1] Accept unsimplified expression. May be calculated in the variance, FT their table with at least 5 probabilities, 0 < p < 1, that sum to 1. FT acceptable at the bold partially evaluated stage.
6. [M1] Appropriate variance formula using their (E(X))² value. FT their table with at least 4 probabilities, 0 < p < 1, that may not sum to 1. FT acceptable at the bold partially evaluated stage. Note: if table is correct, 22.6 – (4.4² or 19.36) implies this M1.
7. [A1] CAO 81/25, 3 6/25 scores A0. Only dependent upon previous M1 (M0 M1 A1 possible). If M0 M0 scored, SC B1 for 3.24 WWW.