Anthony owns Stock A. Suppose that on any given day, the price of Stock A will e

Question

Anthony owns Stock A. Suppose that on any given day, the price of Stock A will either go up or down by 1 unit with equal probability. Also assume that the daily movements in price are independent over different days. (a) What is the probability that the stock price has gone up by 1 unit after 3 days? (b) Suppose that after 3 days, the stock price has gone down by 1 unit. What is the probability that the price went up on the first day? (c) Anthony's friend, Brandon, owns Stock B. On each day, the price of Stock B will either go up or down by 1 unit. The probability that the price will go up on a single day is 0.3. Again, the daily movements in price are independent over different days.

Explanation / Answer

[only third question is done]

3. c) there are two stocks A and B

one stock is randomly chosen.

so P[A]=0.5 P[B]=0.5

for stock A , the price will either go up or go down by 1 unit with equal probability and daily movements in price are independent over different days.

for stock B, the probability that price will go up on a single day is 0.3 hence the probability for going down is 1-0.3=0.7. here also daily movements in price are independent over different days.

after 3 days the price of the chosen stock has gone down by 1 unit.

let D denotes the event that after 3 days the price of the chosen stock has gone down by 1 unit.

hence out of the 3 days , in 2 days the stock has gone down and in one days stock has gone up

these 2 days out of the 3 days can be selected in 3C2 ways.

so P[D|A]=3C2(0.5)2(0.5)1=0.375

P[D|B]=3C20.720.31=0.441

we need to find the probability that the selected stock is A.

so here Bayes' theorem is applied.

so P[A|D]=P[D|A]*P[A]/[P[D|A]*P[A]+P[D|B]*P[B]]=0.375*0.5/(0.375*0.5+0.441*0.5)=0.4595588 [answer]

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