A group of people at a health club were classified according to their gender and

Question

A group of people at a health club were classified according to their gender and smoking habits, as shown below: One person is selected at random from that group of for people. Find the following probabilities and write the corresponding events in symbols (using intersections, unions, etc such as P(M intersection S)). I. What is the probability that the person smokes? II. What is the probability that the person is female but does not smoke? III. What is the probability that the person is male and smoker or a female and smoker? IV. If the person was female, what is the probability that she does not smoke?

Explanation / Answer

Part (1)

Probability the randomly selected person is a smoker = P(S) = Number of smokers/total number of persons in the group = 8/40 = 0.2 ANSWER

Part (2)

Probability the randomly selected person is a female but does not smoke = P(F NS)

= Number of female non-smokers/total number of persons in the group = 8/40 = 0.2 ANSWER

Part (3)

Probability the randomly selected person is a male who smokes or a female who smokes

= P[(M S) (F S)]

= (Number of male smokers + Number of female smokers) /total number of persons in the group = (2 + 6)/40 = 0.2 ANSWER

Part (4)

Given that the randomly selected person is a female, probability she does not smoke

= P[NS/F]

= Number of female non-smokers /total number of females in the group = 8/14 = 0.57 ANSWER

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