An investor has stocks of 10 different companies in her port

An investor has stocks of 10 different companies in her portfolio. Of these companies, 7 are industrial and 3 are utility. She decides to sell stocks of four of these companies. If she picks the companies at random, find the probability that:There will be equal number of industrial and utility companies in her selection.All utility stocks are in the selection.Suppose GE is one of the 10 companies in her portfolio, what is the probability that she keeps the GE stock without selling?

Solution

a)

There are 10C4 ways to pick any 4.

There are (7C2)*(3C2) ways to choose 2 of each kind.

Thus,

P(equal number) = [(7C2)*(3C2)]/[10C4] = 0.3 [answer]

********************

b)

If all 3 utilities are in, then there are just 7 ways to choose the fourth one.

Thus,

P(all 3 utility) = 7 / 10C4 = 0.033333333 [answer]

********************

c)

There are 9C4 ways to choose 4 non-GE\'s.

Thus,

P(not GE) = (9C4) / (10C4) = 0.6 [answer]