## Edu Mock test II-QNo-2

tell2rekha
Posts: 3
Joined: Wed Oct 22, 2014 5:58 pm

### Edu Mock test II-QNo-2

Sam, an analyst at Alpha Catalyst fund, finds out the following statistics based on historical data. Only 20% of subsidiaries of Alpha Catalyst are in the ‘Elite list’ published by their newsletter. The rest of subsidiaries are termed ‘Ordinary’. The probability that an elite company records a profit in any given year is 80%. For an ordinary company, there is as much chance to make a profit as it is to make a loss. For both the type of companies, the probability of making a profit is independent from one year to the next.
Now consider a subsidiary which was established 2 years ago and has recorded a profit in both the years. What is the probability that the subsidiary is in elite list now?

edupristine
Finance Junkie
Posts: 722
Joined: Wed Apr 09, 2014 6:28 am

### Edu Mock test II-QNo-2

Sol. Only 20% of the total subsidiaries are in elite list. So the probability that a random company is in elite list is:

P(E) = 0.2 ; P(O) = 0.8

The probability that the company earns a profit given that it is in elite list is

P(P/E) = 0.8

The probability that the company earns a profit given it is ordinary is P(P/O) = 0.5

We need to find out the probability that the company is in elite list, given that it has earned profit consecutively twice i.e. P(E/2P)

Now P(E/2P) = (P(2P/E)*P(E))/(P(2P))

P(2P/E) = 0.8*0.8 = 0.64

P(2P) = P(P/E)xP(E) + P(P/O)x P(O) = 0.82 * 0.2 + 0.52 * 0.8 = 0.328

So P(E/2P) = (0.64 * 0.2)/0.328 = 0.39