Probability Q

Pen sean SG

A team of five analysts is about to examine the earnings prospects of 20 corporations. Each of the five analysts will study 4 of the corporations. These analysts are not equally competent. In fact, one of them is a star, having an excellent record of anticipating changing trends. Ideally, management would like to allocate to this analyst the 4 corporations whose earnings will deviate most from past trends. However, lacking this information, management allocates corporations to analysts randomly.

Q what is the probability that at least 2 of the 4 corporations whose earnings will deviate most from the past trends are allocated to the star analyst?

skythewood SG

probability star will choose all 4 = nCr 4/20 x 3/19 x 2/18 x 1/17

probability star will choose only 3 = nCr 4/20 x 3/19 x 2/18 x 16/17

probability star will choose only 2 = nCr 4/20 x 3/19 x 16/18 x 15/17

edit: add in nCr = 4C4/ 4C3/ 4C2

Mikethm SG

sky read your pm pls

skythewood SG

yup, mike, yours is right

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Probability that star is not allocated any

= 16/20 x 15/19 x 14/18 x 13/17

= 364/969

Probabiltity that star is allocated only 1 of the 4 corporations

= (4/20 x 16/19 x 15/18 x 14/17) + (16/20 x 4/19 x 15/18 x 14/17) + (16/20 x 15/19 x 4/18 x 14/17) + (16/20 x 15/19 x 14/18 x 4/17)

= 448/969

Probability that at least 2 are allocated to star

= 1 -364/969 - 448/969

= 157/969

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