a pharmaceutical company conducted a study to evaluate the effect of an allergy relief medicine; 250 patients with symptoms that included itchy eyes and a skin rash received the new drug. the results of the study are as follows: 90 of the patient's treated experienced eye relief, 135 had their skin rash clear up, and 45 experienced relief of both itchy eyes and the skin rash. what is the probability that a patient who takes the drug will experience relief of at least one of the two symptoms?

Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.

probability = desired outcome / total outcomes

If 90 of the patient's treated experienced eye relief and 45 experienced relief of both itchy eyes and the skin rash, then 45 experienced eye relief only.

eye relief only = 90 - 45 = 45

If 135 had their skin rash clear up, and 45 experienced relief of both itchy eyes and the skin rash, then 90 had their skin rash clear up only.

skin rash clear up only = 135 - 45 = 90

Hence, the total number of patients who took the drug and experienced relief of at least one of the two symptoms is 180.

45 + 90 + 45 = 180

Divide by the total number of patients.

probability = desired outcome / total outcomes

probability = 180 / 250

probability = 0.72

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