In: Finance
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 |
|||
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
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)