Question

Each day the price of a stock goes up a dollar with probability .75, or down a dollar with probability .25. Assuming these fluctuations to be independent, what is the probability that after 6 days the stock will be trading at the same price? What is the probability that it will have gone down?

How can I do it in Microsoft Excel?

Answer 1

1)this is a binomial distribution with p=0.75 and n=6

probability that after 6 days the stock will be trading at the same price =P(X=3)=P(stock has exactly 3 up and 3 down)

= $\small \binom{6}{3}(0.75)^{3}(0.25)^{3}$ =0.1318

(Note : you can use excel function: =binomdist(3,6,0.75,false)

2)

probability that it will have gone down =P(at most 2 ups) =P(X<=2) = $\small \sum_{x=0}^{2}\binom{6}{x}(0.75)^{x}(0.25)^{6-x}$ =0.0376

(Note : you can use excel function: =binomdist(2,6,0.75,true)