3) An investor has stocks of 10 different companies in her portfolio. Of these c

Question

3) 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: a) There will be equal number of industrial and utility companies in her selection. b) All utility stocks are in the selection c) At least one utility stock is in her selection. d) Suppose "XYZ Inc." is one of the 10 companies in her portfolio and she decides to sell four stocks. What is the probability that she keeps the "XYZ Inc." stock without selling?

Explanation / Answer

Solution:

total number of possible wys of selecting 4 out of 10 companies = 10C4 = 210

( a )

Probability that selecting equal number of indestrial and utility compnies = 7C2 * 3C2 / 10C4 = 21 * 3 /210= 63/210 = 0.3

( b )

probability that all utility stocks are selected = 7C1 * 3C1 / 10C4= 7 *1 / 210 = 0.0333

( c )

probability that atleast one utility stock is selected = 1 - probability that no utility scock is selected

= 1 - ( 7C4 / 10C4) = 35 /210 = 0.1666

( d )

probability that she does not sell XYZ inc = 9C4 / 10C4 = 126 / 210 = 0.6

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