nat 4.25)A study by the ASX revealed that 39% of the stralian adult population a

Question

nat 4.25)A study by the ASX revealed that 39% of the stralian adult population are shareholders. In addition, the study determined that 71% of all Australian adult shareholders have postgraduate education. Suppose 5% of all Australian adults have postgraduate education. An Australian adult is randomly selected. What is the probability that th adult: a, does not own shares b. owns shares and has postgraduate education c. owns shares or has postgraduate education d. has neither postgraduate education nor owns shares e. does not own shares or has no postgraduate uld 24 education f. has postgraduate education and owns no shares? e?

Explanation / Answer

Given information:

P(shareholder) = 0.39

P(postgraduate | shareholder) = 0.071

P(postgraduate) = 0.05

(a)

By the complement rule, the probability that the adult does not own shares is

P(not shareholder) = 1 - P(shareholder) = 1 - 0.39 = 0.61

(b)

P(postgraduate and shareholder) = P(postgraduate | shareholder) P(shareholder)= 0.071 * 0.39 = 0.02769

(c)

P(postgraduate or shareholder) =P(postgraduate)+P(shareholder)-P(postgraduate and shareholder) = 0.05+0.39 - 0.02769 = 0.41231

(d)

By the complement rule,

P[not (postgraduate or shareholder)]=1-P(postgraduate or shareholder)=1 - 0.41231 = 0.58769

(e)

P(not shareholder) = 1 - P(shareholder) = 1 - 0.39 = 0.61

P(not postgraduate) = 1 - 0.05 = 0.95

P(not shareholder or not postgraduate) = P(not shareholder)+P(not postgraduate) - P[not (postgraduate or shareholder)] = 0.61+0.95 - 0.58769 = 0.97231

(f)

P(postgraduate and no share)= P(postgraduate) - P(postgraduate and shareholder) = 0.05 - 0.02769 = 0.02231

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