5 Each morning I reach into my box of tea bags and, without looking, randomly choose a bag. The bags are manufactured in pairs, which can be separated along a perforated line. So when I choose a bag it might be attached to another, in which case I have to separate them and return the other bag to the box. Alternatively, it might be a single bag, having been separated on an earlier day. I only use one tea bag per day, and the box always gets thoroughly shaken during the day as things are moved around in the kitchen. You are to simulate this process, starting with 5 double bags and 0 single bags in the box. You are to use single-digit random numbers in your simulation.

1. On day 2 there will be 4 double bags and 1 single bag in the box, 9 bags in total. Give a rule for simulating whether I choose a single bag or a double bag, assuming that I am equally likely to choose any of the 9 bags. Use single-digit random numbers in your simulation rule.
2. On day 3 there will either be 4 double bags or 3 double bags and 2 single bags in the box. Give a rule for simulating what sort of bag I choose in the second of these cases. Use single-digit random numbers in your simulation rule.
3. Using the random digits in your answer book, simulate what happens on days 2,3 and 4 , briefly explaining your simulations. Give an estimate of the probability that I choose a single bag on day 5 .
4. Using the random digits in your answer book, carry out 4 more simulations and record the results.
5. Using your 5 simulations, estimate the probability that I choose a single bag on day 5 .
   [0pt] [Question 6 is printed overleaf.]