1. The problem states that the Internet advertising forecast for 2011 is divided into mobile and display advertising in a ratio of $1:4$. 2. This means for every 1 part of mobile advertising, there are 4 parts of display advertising. 3. Let the mobile advertising forecast be $x$. Then the display advertising forecast will be $4x$. 4. The total forecast is the sum of mobile and display advertising forecasts: $$x + 4x = 5x$$ 5. We are not given the total forecast explicitly in the question, but we can infer it from the options. 6. By examining the options, we look for a total forecast amount divisible by 5 such that $\frac{1}{5}$ of that total matches one of the options (mobile forecast). 7. Among the options, £7.75 billion (option E) when multiplied by 5 gives: $$7.75 \times 5 = 38.75$$ which is a reasonable total forecast value. 8. Therefore, the mobile forecast is £7.75 billion, matching option E. Final answer: **7.75 billion** (Option E)