NOEVENTS ARE CONSIDERED BY STOCK ANALYSTS, SAY R-[REAL ESTATE MARKET WILL GROw]

Question

NOEVENTS ARE CONSIDERED BY STOCK ANALYSTS, SAY R-[REAL ESTATE MARKET WILL GROw] AND M- [MORTGAGE INTEREST RATE WILL DECREASE]. THEY ASSESSED THE PROBABILITY OF THE EVENT R AS 35%, AND THE PROBABILITY OF THE EVENT M AS 28%, IN THE MEANTIME, THE CHANCE THAT AT LEAST ONE EVENT WILL OCCUR (THAT IS THE UNION, R ORM) IS CONSIDERED AS 42%. 1. WHAT IS THE CHANCE THAT TWO EVENTS, R AND M, WILL OCCUR JoINTLY? PIR AND M BOTH WILL OCCUR- 2. FILL THE TABLE OF JOINT AND MARGINAL PROBABILITIES MARGINAL M occURS M DOES NOT OCCUR R OCCURS R DOES NOT OCCUR MARGINAL 0.35 .65 1.00 0.28 72

Explanation / Answer

Solution:

    We are given that :

R = Real Estate Market Will Grow
M = Mortagage interest rate will Decrease
P(R ) = 0.35
P(M ) = 0.28
P( R or M ) = 0.42

Part 1) Find P( R and M) = ............?

Thus from given information , using Addition rule of probability we get :

P( R or M) = P(R) + P(M) - P( R and M)

0.42 = 0.35 + 0.28 - P( R and M)

0.42 = 0.63 - P( R and M )

P( R and M) = 0.63 - 0.42

P(R and M) = 0.21

Part 2) Fill the joint and marginal probabilities:

Thus final table is:

M Occurs M does not occur Marginal R Occurs P(R and M)=0.21 =0.35-0.21=0.14 0.35 R does not Occur =0.28-0.21=0.07 =0.72-0.14=0.58 =1.00-0.35=0.65 Marginal 0.28 =1.00-0.28=0.72 1.00

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