An investor holds two stocks, each of which can rise (r), remain unchanged (u), or decline (d) on any particular day. assume that for the first stock (on a particular day)

p(r) = 0.2 , p(u) = 0.6 , p(d ) = 0.2

and that for the second stock (on a particular day)

p(r) = 0.3 , p(u) = 0.4 , p(d ) = 0.3

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.)

both decline =

exactly one rises =

exactly one unchanged =

both rise =

1. 0.06

2. 0.38

3. 0.52

4. 0.06

Explanation:

1) Both decline = P1(D) × P2(D)

                         = 0.2 × 0.3

                         = 0.06

(stock 1 declines and stock 2 declines)

2) Exactly one rises:

= P1(R) × [P2(U) + P2(D)] + P2(R) × [P1(U) + P1(D)]

= 0.2 × [0.4+ 0.3] + 0.3 × [0.6 + 0.2]

= 0.14 + 0.24

= 0.38

(stock 1 rises and {stock 2 declines or remains unchanged})

or (stock 2 rises and {stock 1 declines or remains unchanged})

3) Exactly one unchanged:

= P1(U) × [P2(R) + P2(D)] + P2(U) × [P1(R) + P1(D)]

= 0.6 × [0.3 + 0.3] + 0.4 × [0.2 + 0.2]

= 0.36 + 0.16

= 0.52

4) Both rise = P1(R) × P2(R)

                   = 0.2 × 0.3

                   = 0.06

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