Question

Whatever be the condition of the economy, the financial markets have been improving very quickly. An investor with the
ability to buy assets is looking at a portfolio and finds that the probability of stock A increasing in value is 50.6%. She also
finds that if stock A increases in value then there is a 55% chance that stock B will also increase. However, if Stock A does
not increase in value, then B increases in only 25% of the times.
a) (3) Find the probability that both A and B increase in value.

b) (3) Find the probability of B increasing in value.

c) (3) Find the probability that either A or B or both increase in value.

d) (3) Find the probability that A increases in value, given that B increased.

e) (2) Are these stocks mutually exclusive? Show evidence to support your answer.

f) (2) Are these stocks statistically independent? Show evidence to support your answer.

g) (2) Are these stocks collectively exhaustive? Show evidence to support your answer.

Answer 1

a) probability that both A and B increase in value=P(A increase)*P(B increase|A increase)

=0.506*0.55=0.2783

b)probability of B increasing in value =P(A increase)*P(B increase|A increase)+P(A not increase)*P(B increase|A not increase)=0.506*0.55+(1-0.506)*0.25=0.4018

c)

probability that either A or B or both increase in value=P(A incerase)+P(B increase)-P(both increase)

=0.506+0.4018-0.2783=0.6295

d)

probability that A increases in value, given that B increased =P(A increase|B increase)

=P(both increase)/P(B In crease)=0.2783/0.4018=0.6926

e)

here as P(A increase n B increse ) is not equal to 0 therefore these stocks are not mutually exclusive

f)

P(A increase)*P(B increase)=0.506*0.4018=0.2033 which is not equal to P(A increase and B increase) therefore A and B are not independent

g)

for P(either A or B or both increase) is not equal to 1 ; therefore  these stocks are not collectively exhaustive