Question

A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 25%. She also believes that if the economy encounters a recession, the Must show the sample space.

1. Find the probability that the mutual fund's value will increase.

2. If there is not a recession what is the probability that the mutual funds does not increase in value?

3. What is the probability that there isn't a recession and the mutual fund increases in value?

4. What is the probability of no recession in the next 12 months?

Answer 1

Solution:

a) the probability that the mutual fund's value will increase.

	Recession	No recession	Total
Increase in value	20	75	20 + 75 = 95
No increase in value	25 - 20 = 5	75 - 75 = 0	100 - 95 = 5
Total	25	100 - 25 = 75	100

P(recession and increase)+P(no recession and increase) =0.25*0.2+(1-0.25)*0.75=0.6125

b) probability that the mutual funds does not increase in value

P(mutual funds does not increase in value given no  recession) =1-0.75 =0.25

c) the probability that there isn't a recession and the mutual fund increases in value

probability that there isn't a recession and the mutual fund increases in value =(1-0.25)*0.75=0.5625

d)  the probability of no recession in the next 12 months

probability of no recession in the next 12 months =1-P(recession) = 1-0.25 =0.75