(a) On his way to catch a bus to work each morning, Mr Adams will sometimes buy a newspaper, and will sometimes buy a sandwich. The probability that he buys a newspaper is 0.5, and the probability that he buys a sandwich is 0.3. Buying a newspaper and buying a sandwich are independent events. The probability that Mr Adams misses his bus is 0.1. However, if he buys a newspaper this may delay him, and so on days when he buys a newspaper the probability that he misses his bus is 0.15.
(i) Calculate the probability that Mr Adams buys a newspaper and buys a
sandwich. [2]
(ii) Calculate the probability that Mr Adams buys a newspaper or buys a
sandwich. [2]
(iii) Calculate the probability that Mr Adams misses the bus and buys a
newspaper. [3]
(iv) Calculate the probability that Mr Adams has bought a newspaper if he
has missed the bus. [3]

(b) (i) Give one advantage and one disadvantage of using the expected value of
a probability distribution. [2]
(ii) An ice cream vendor finds that sales of ice cream each day satisfy the
following distribution:

If each ice cream is sold for $2, calculate the expected takings of the
vendor each day. [3]