Question

4. Suppose that 78% of people enjoy drinking coffee and 44% of people enjoy drinking tea. In addition, 39% of people that enjoy drinking coffee also enjoy drinking tea. Let C represent the event that a person enjoys drinking coffee, and I represent the event that a person enjoys drinking tea. In each part of this question, you must first express each probability in terms of the events C and T and justify any computation through the use of a formula (a) Express each of the three probabilities listed above in terms of the events C and T. (b) Are C and 7 independent events? Explain your answer using only the probabilities from part (a). Do not calculate any other values. (c) What proportion of the people enjoy drinking both coffee and tea? (d) If a person enjoys drinking coffee, what is the probability they do not enjoy drinking tea? (e) If a person does not enjoy drinking tea, what is the probability they enjoy drinking coffee?

Answer 1

a) P(C) = 0.78

P(T) = 0.44

P(C and T) = 0.39

b) P(C) * P(T) = 0.78 * 0.44 = 0.3432

Since P(C and T) $\neq$ P(C) * P(T), so the events C and T are not independent.

c) P(C and T) = 0.39

d) P(T' | C) = P(T' and C)/P(C)

= (P(C) - P(T and C))/P(C)

= (0.78 - 0.39)/0.78

= 0.39/0.78 = 0.5

e) P(C | T') = P(C and T')/P(T')

= (P(C) - P(C and T))/(1 - P(T))

= (0.78 - 0.39)/(1 - 0.44)

= 0.39/0.56

= 0.6964