Answer to Question #132282 in Statistics and Probability for David

Question

In a group of 78 people; 24 drink tea and 31 drink coffee. Find the probability that a person picked from this group at random is either tea or coffee drinker?
Find answer in fractions form.

Answer 1

The probability that a person does not drink tea is $1-24/78=54/78.$ The probability that a person does not drink coffee is $1-31/78=47/78.$ Hence, the probability that a person does not drink coffee or tea equals $54/78\cdot47/78=54\cdot47/78^2=3\cdot47/(26\cdot13)=141/338.$ The probability that a person is tea or coffee drinker equals $1-141/338=197/338.$