 Business
20 May, 05:00

# 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) = 0.2and that for the second stock (on a particular day)P (R) = 0.3, P (U) = 0.4, P (D) = 0.3Assuming 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 =

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1. 20 May, 05:23
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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