You and your friend are presented with 7 boxes. 3 of the boxes contain delicious

chocolates while the other 4 are filled with deadly mushrooms (disguised as delicious

chocolates). Both of you will need to select a box and eat what is inside, but you need to

decide which of you will go first.

(i) In order to increase your chance of eating delicious chocolates, should you choose first

or second? Answer this by defining your notation and using conditional probabilities (not

by using tree diagrams) with results from the module.

(ii) If you choose first, what is the probability that you eat delicious chocolates, given that

your friend also does? Use similar techniques to part (i).

(iii) How would your answer to (i) change if there were three of you: yourself and two

friends? Answer this without doing any mathematics or algebra, perhaps by referring to

examples from the module.