Roman is considering buying shares of GHI stock. The stock currently sells for $60 per share. The stock changes in value at 8:00 am each day, either increasing in value by $10 or decreasing in value by $1. The stock will increase in value with 90% probability, and decrease in value with 10% probability. The stock follows a random walk. In three days, what is the probability that GHI is less than $70?

The Probability that the GHI is less than $70 in three days is 1% or 0.01

Step-by-step explanation:

Here, we want to find the probability that the GHI is less than $70.

So what we do here is to find the scenarios that could make the $60 less than $70 is three days;

Scenario 1;

Two days decrease and one day increase

That will bring the value to 60 -1-1 + 10 = $68 which is less than 70

Scenario 2;

Three days decrease

That will bring the value to

60-1-1-1 = 57 which is less than 70

Any other possible scenario to make the value of the share less than 70? NO !

For the 1st case scenario;

Two days decrease and one day increase;

The scheduled probabilities will be as follows;

Kindly recall, probability of increase = 90% = 90/100 = 0.9

Probability of decrease = 10% = 10/100 = 0.1

So probability in scenario 1 will be;

P(Two days decrease and one day increase)

= 0.1 * 0.1 * 0.9 = 0.009

Kindly note this can happen in any order and since no order was specified, we do not need to consider other cases

Scenario ii

Three days decrease

That will be;

P(three days decrease) = 0.1 * 0.1 * 0.1 = 0.001

So the addition of both since we will be having either of the two and or means addition in probability will be ;

0.001 + 0.009 = 0.01 = 1%