7. During a convention of the American Statistical Association, the the politica

Question

7. During a convention of the American Statistical Association, the the political preferences and sex of each conventioneer and obtains the following results. Males: Females: Democrats 30 45 Republicans 20 30 Libertarians 40 60 (a) Find the probability of randomly selecting a Male and a Democrat. Are sex and politics statistically independent? (b) If the selected conventioneer is a Democrat what is the probability that he is a Male? (c) What is the probability of selecting either a Male or a Democrat? Are the events of selecting a male and event of selecting a Democrat mutually exclusive?

Explanation / Answer

Total table

(a) Pr(A male and a democrate) = Total such people/Total number of people = 30/225 =  0.1333

Here Pr(Male and democrate) = Pr(Male) * Pr(democrate l Male) = (90/225) * (30/90 = 30/225 = 0.1333

so yes sex and politics are statistically independent here.

(b) Pr(Male l Democrate) = TOtal number of male democrats / Total number of democrate = 30/(30 + 45) = 30/75 = 2/5 = 0.4

(7) Pr(EIther male or democrate) = Pr(Male) + Pr(Democrate) - Pr(Male and democrate)

= 90/225 + 75/225 - 30/225 = 0.6

If both events are mutually exclusive than both events can't occur simultanoursly so as

Pr(Male and democrate) 0

so these events are not mutually exclusive.

Democrats Republicans Libertarians Total Males 30 20 40 90 Females 45 30 60 135 Total 75 50 100 225

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