Question

80 students were interviewed, of which 35 had alcohol and 18 drug problems and five had both conditions. if one of these patients is selected at random, what is the probability that: a. not be an alcoholic, b. do not have any of these two conditions, c. have only these two conditions, c. have only alcohol problems, d. have at least one of the two conditions, e. have exactly one of the two conditions

Answer 1

Total students = 80

People with alcohol problem = 35

People with drug problem = 18

People with both = 5

People with neither condition = 80 - 35 - 18 - 5 = 22

Therefore, we know that

Probability = No of people with condition/ total number of people

Therefore,

a)

Number of people without alcohol problem = 80 - 35 - 5 = 40

Therefore, probability = 40/80 = 1/2

b)

Number of people without any condition = 22

Therefore, probability = 22/80 = 11/40

c)

Number of people with both condition = 35 + 18 + 5 = 58

Therefore, probability = 58/80 = 29/40

c)

people with only alcohol as a problem = 35

Therefore, probability = 35/80 = 7/16