Rachel has three coins. The first coin is biased so that the probability of obtaining a head when it is thrown is. The second coin is biased so that the probability of obtaining a head when it is thrown is 4. The third coin is fair. Rachel throws the three coins at the same time. The random variable X is the number of tails that she obtains.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [B1] Table with correct values of x and at least one non-zero probability correct. Condone extra x values if probability stated as 0.
2. [B1] Two more correct non-zero probabilities linked with correct outcome (3 correct probabilities present). Accept probabilities not in table if clearly identified.
3. [B1] Four correct probabilities linked with the correct outcomes. Accept probabilities not in table if clearly identified. Non-exact decimals correct to at least 3SF. SCB1 for 4 non-zero probabilities (not all 4) in table with correct x values adding to 1 if B1 max scored.