Irena Davies manages a portfolio of 200 ordinary shares. Her staff classified the portfolio of shares...

Irena Davies manages a portfolio of 200 ordinary shares. Her staff classified the portfolio of shares by ‘industry sector’ and ‘investment objective’.

Investment Objective	Industry Sector
Investment Objective	Electronics	Airlines	Healthcare	Total
Growth	100	10	40	150
Income	20	20	10	50
Total	120	30	50	200

Are 'Healthcare' and 'Income' independent, why or why not?

Select one:

No, because P(Healthcare | Income) ≠ P(Healthcare)

No, because P(Healthcare) ≠ P(Income)

Yes, because P(Healthcare ∩ Income) = P(Healthcare) P(Income)

Yes, because P(Healthcare ∩ Income) ≠ 0

Solutions

Expert Solution

The formula for probability of an eveny E as follows

P(E)=(number of favourable outcomes)/(total number of outcomes)

Independent events:

The events A and B are said to be independent if the result of one event doesnot depend on the result of another event.

In other words ,The occurance or non occurance of event A doesnot affect the occurance and non occurance of event B and vice versa

If A and B are independent,then P(A/B)=P(A) or P(B/A)=P(B)

Consider the probability,P(Health care/Income)

using the conditional probability,

P(healthcare/income)=P(health care and income)/P(income)

=(10/200)/(50/200)

=10/50

=0.2

P(Healthcare/income)=0.2

Now consider the probability of P(health care )

P(Health care)=50/200

=0.25

That is P(healthcare/income) doesnot equal to p(Healthcare)

Thus the events health care and income are not independent

So the answer is NO,Because P(Health care/income) not equal to P(Health care)

jeff jeffy answered 2 years ago

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