Question

If we start at a price of four dollars, with price movements of 1 dollar and 3 price movements; if the probability of up is .8 and the probability of down is .2. then what is the probability of a path (just an individual one) ending at 5 dollars?

a. .032
b. .125
c. .0625
d. .128

Answer 1

The probability of a path ending at $5 in this scenario is 0.64.

Step-by-step explanation:

To find the probability of a path ending at $5, we need to consider the possible movements and their probabilities. The starting price is $4, with 3 price movements of $1 each. The probability of an up movement is 0.8, and the probability of a down movement is 0.2.

Starting at $4, there are two possible paths that end at $5: Up, Up, Up and Up, Down, Up. We can calculate the probability of each path by multiplying the probabilities of each movement. For the Up, Up, Up path, the probability is 0.8 * 0.8 * 0.8 = 0.512. For the Up, Down, Up path, the probability is 0.8 * 0.2 * 0.8 = 0.128.

To find the total probability of ending at $5, we add the probabilities of the two paths: 0.512 + 0.128 = 0.64. Therefore, the probability of a path ending at $5 is 0.64.