A stockbroker has determined from recent records of a certain stock that, on any

Question

A stockbroker has determined from recent records of a certain stock that, on any given day, the stock rises (R) with probability 0.3, falls (F) with probability 0.1, or remains unchanged (U) with probability 0.6. Assume that the movements (R, F, U) of the sock from day to day are independent; no matter what happens to the stock today, its behavior tomorrow or on subsequent days is not affected. a) Find the probability that the stock rises three days in a row. b) Find the probability that the stock falls on one day, rises the next day, and remains unchanged the third day. c) Find the probability that the stock falls exactly one day out of the next two days. d) Find the probability that the stock behaves the same way two days in a row

Explanation / Answer

P(R) = 0.3

P(F) = 0.1

P(U) = 0.6

A) probability of stock rises 3 days in a row = P(R)3

= 0.33

= 0.027

B) probability that stock falls on 1st day, rises next day and remains unchanged the third day = P(F) * P(R) * P(U)

= 0.1*0.3*0.6

= 0.018

C) probability that the stock falls exactly one day out of the next two days = P(F) * (1 - P(F))

= 0.1 * (1 -0.1)

= 0.09

D) probability that the stock behaves the same way two days in a row = P(R)2 + P(F)2 + P(U)2

= 0.32 + 0.12 + 0.62

= 0.46

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