Question

A stall sells cups of coffee, which may be caffeinated or decaffeinated, and may contain milk or be milk-free. It turns out that:

• 60% of the cups of coffee sold at the stall contain milk;

• of those cups of coffee sold at the stall containing milk, 24% are also decaffeinated.

(a) Let A denote the event that a cup of coffee sold at the stall contains milk, and let B denote the event that a cup of coffee sold at the stall is decaffeinated. Write the information given in the two bullet points above using probabilities in symbolic form.

(b) Calculate the probability that a randomly selected coffee sold at the stall both contains milk and is decaffeinated.

(c) Additional information is now given that 35% of coffees sold at the stall are decaffeinated. Calculate the probability that a randomly selected coffee sold at the stall that is decaffeinated also contains milk.

(d) What percentage (to the nearest whole percent) of coffees sold at the stall either contain milk, or are decaffeinated, or both?

(e) For coffees sold at this stall, are the events of containing milk and being decaffeinated independent? Give a reason for your answer.

Answer 1