Zachros A.

asked • 09/27/14# the consultant tells the investor interest rates will stay the same, what probability should the investor attach to the event that they actually will increase?

An investor is unsure whether interest rates will increase (I), remain the same (S), or decrease (D) by mid-summer. Based on his own experience, he attaches the following probabilities to these events: P(I) = .4, P(S) = .3, and P(D) = .3. However, he decides to purchase the advice of a consultant. The consultant’s “track record” is summarized below.

The consultant’s “track record” is summarized below.

P(CI | I)=.7 P(CI | S)=.4 P(CI | D)=.2

remain the same (CS) P(CS | I)=.2 P(CS | S)=.5 P(CS | D)=.2

decrease (CD) P(CD | I)=.1 P(CD | S)=.1 P(CD | D)=.6

More

## 1 Expert Answer

Dattaprabhakar G. answered • 09/28/14

Tutor

5
(2)
Expert Tutor for Stat and Math at all levels

Zachros:

In the language of the problem, you want P(I | CS) = P ( I, CS) / P(CS) = P( CS | I)P(I)]

Now

P(I | CS) = P ( I, CS) / P(CS) Formula for conditional probability,

P(CS) = P( CS | I)P(I) + P( CS | S)P(S) + P( CS | D)P(D) Formula for total probability.

Also

= P ( I, CS)) = P( CS | I)P(I), again, using the formula for conditional probability.

The question has provided us the (marginal) prababilities P(I), P(S) and P(D) based on investor's experience.

Therefore, we compute the answer as

P(I | CS) = P( CS | I)P(I) / [P( CS | I)P(I) + P( CS | S)P(S) + P( CS | D)P(D) P(CS)]

= [0.2 x 0.4] / {0.08 + 0.15 + 0.06} = 0.08 / 0.29 =

**0.276.**Please check my computations and confirm the answer by posting a comment, Thanks.

Dr. G.

## Still looking for help? Get the right answer, fast.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

#### OR

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

Dattaprabhakar G.

P(I | CS) = P ( I, CS) / P(CS) = P( CS | I)P(I)]

09/28/14