What is the probability that the business makes a profit in exactly two of its first three years?
Assume that the business makes a profit with probability 0.3 in the first year. For each year thereafter, the business makes a profit with probability 0.7 if it made a profit in the previous year, and with probability 0.2 if it did not make a profit in the previous year.
What is the probability that the business makes a profit in exactly two of its first three years?
There are only three ways that can happen:
It profits in years (one and two but not three) or (one and three but not two) or (not one, but two and three).
“Or” means add, so we just need to figure out the things in the parentheses and add them.
If we follow the map they laid out carefully, the first parenthetical set is 0.3×0.7×0.3.
The second set is 0.3×0.3×0.2.
The third is 0.7×0.2×0.7.
So these are 0.063+0.18+0.098 = 0.341.
Recheck my math!