Question

Probability that stock A ends the day with a price below K20 is 40%. The probability stock B ends the day with a price below K20 is 25%. The probability stock A ends the day with a price below K20 given stock B ends the day with a price below K20 is 60%. Calculate the probability stock A or stock B ends the day with a price below K20.      

Answer 1

Solution:-

Let the events that stock A and stock B ends thee day with a price below K20 be denoted by A and B .

Now,

Since probability that stock A ends the day with a price below K20 is 40%.

So, P(A) = 0.40 .....(1)

Since the probability stock B ends the day with a price below K20 is 25%.

So, P(B) = 0.25 .....(2)

Since the probability stock A ends the day with a price below K20 given stock B ends the day with a price below K20 is 60%.

So, conditional probability P(A/B) = 0.60 .....(3)

We know that conditional probability of A if B is given is goven by

This implies

On putting the values from equations (2) and (3), we get

........(4)

Now, the probability that stock A or stock B ends the day with a price below K20 is given by P(AUB).

We know that

On putting the values from equations (1), (2) and (4), we get

Hence, Probability that stock A or stock B ends the day with a price below K20 is 50%.