An investor holds two stocks, each of which can rise ( R ), remain unchanged ( U

Question

An investor holds two stocks, each of which can rise (R), remain unchanged (U), or decline (D) on any particular day.

Assuming that these stocks move independently, find the probability that both stocks decline; the probability that exactly one stock rises; the probability that exactly one stock is unchanged; the probability that both stocks rise. (Round your answers to 2 decimal places.)

Assume that for the first stock (on a particular day)                                                      P(R) = 0.5 , P(U) = 0.4 , P(D ) = 0.1 and that for the second stock (on a particular day)                                                      P(R) = 0.3 , P(U) = 0.5 , P(D ) = 0.2

Explanation / Answer

a) Probability that both the stocks decline

= ( Probability that the first stock decline ) * ( Probability that the second stock decline )

= 0.1*0.2 = 0.02

Therefore 0.02 is the required probability here.

b) Probability that exactly one stock rises:

= ( Probability that the first stock decline and second rises) + ( Probability that the second stock declines and first rises)

= 0.1*0.3 + 0.2*0.5

= 0.03 + 0.1 = 0.13

Therefore 0.13 is the required probability here.

c) Probability that exactly one stock remain unchanged

= ( Probability that first stock remains unchanged and the second one changes ) + ( Probability that the second stock remains unchanged and the first one changes )

= 0.4*(1 - 0.5) + 0.5*( 1-0.4)

= 0.4*0.5 + 0.5*0.6

= 0.2 + 0.3 = 0.5

Therefore 0.5 is the required probability here.

d) Probability that both stocks rises = 0.5*0.3 = 0.15

Therefore 0.15 is the required probability here.

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