Answer:
0.0667 = 6.67% probability that the shares of a company that fires its CEO will increase by more than 5%.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
![P(B|A) = \frac{P(A \cap B)}{P(A)}](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D)
In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this problem:
Event A: Company fires the CEO
Event B: Shares increase by more than 5%.
Probability of a company firing it's CEO:
35% of 100 - 4 = 96%(shares did not increase by more than 5%).
60% of 4%(shared did increase by more than 5%).
So
![P(A) = 0.35*0.96 + 0.6*0.04 = 0.36](https://tex.z-dn.net/?f=P%28A%29%20%3D%200.35%2A0.96%20%2B%200.6%2A0.04%20%3D%200.36)
Intersection of events A and B:
Fires the CEO and shared increased by more than 5%, is 60% of 4%. So
![P(A \cap B) = 0.6*0.04 = 0.024](https://tex.z-dn.net/?f=P%28A%20%5Ccap%20B%29%20%3D%200.6%2A0.04%20%3D%200.024)
Probability that the shares of a company that fires its CEO will increase by more than 5%.
![P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.024}{0.36} = 0.0667](https://tex.z-dn.net/?f=P%28B%7CA%29%20%3D%20%5Cfrac%7BP%28A%20%5Ccap%20B%29%7D%7BP%28A%29%7D%20%3D%20%5Cfrac%7B0.024%7D%7B0.36%7D%20%3D%200.0667)
0.0667 = 6.67% probability that the shares of a company that fires its CEO will increase by more than 5%.