Challenging +1.2 This requires setting up a system of equations from the given constraints (probabilities sum to 1, expected value equals £206, and the 2:1 ratio condition), then solving for unknown probabilities. It involves constructing a probability distribution table with profit calculations, but the algebra is straightforward and the problem-solving approach is systematic rather than requiring novel insight. Slightly above average difficulty due to the multi-constraint setup and algebraic manipulation required.
6. Penelope makes 8 cakes per week. Each cake costs \(\pounds 20\) to make and sells for \(\pounds 60\). She always sells at least 5 cakes per week. Any cakes left at the end of the week are donated to a food bank. The probability that 5 cakes are sold in a week is \(0 \cdot 3\). She is twice as likely to sell 6 cakes in a week as she is to sell 7 cakes in a week. The expected profit per week is \(\pounds 206\).
Construct a probability distribution for the weekly profit.
Additional page, if required. number Write the question number(s) in the left-hand margin.
Additional page, if required.
Write the question number(s) in the left-hand margin.
\section*{PLEASE DO NOT WRITE ON THIS PAGE}
6. Penelope makes 8 cakes per week. Each cake costs $\pounds 20$ to make and sells for $\pounds 60$. She always sells at least 5 cakes per week. Any cakes left at the end of the week are donated to a food bank. The probability that 5 cakes are sold in a week is $0 \cdot 3$. She is twice as likely to sell 6 cakes in a week as she is to sell 7 cakes in a week. The expected profit per week is $\pounds 206$.
Construct a probability distribution for the weekly profit.\\
Additional page, if required. number Write the question number(s) in the left-hand margin.
Additional page, if required.
Write the question number(s) in the left-hand margin.
\section*{PLEASE DO NOT WRITE ON THIS PAGE}
\hfill \mbox{\textit{WJEC Further Unit 2 2024 Q6 [7]}}