Question

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 =

Answer 1

Answer:

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