Question

Eva and Ildiko live in a small village in Romania. Eva wants to start a business of making woolen blouses, and she needs a loan in order to buy a sewing machine. Ildiko wants to start a business of growing organic quinoa, and she needs a loan in order to buy a machine for separating the seed from the husk. Ildiko and Ana get loans from a microfinance company.

Ildiko’s business may succeed or fail. Eva’s business may succeed or fail. View these businesses as an experiment. Give the sample space generated by this experiment.

The probability that Ildiko's business will be a success is 0.75. The probability is 0.65 that Eva’s business will be successful. The probability that both businesses will succeed is 0.55. Give the probability distribution over the sample space.

The probability of only Eva succeeding is

The probability that at least one of them succeeds is

The probability that non of them succeeds is

Are the events “Ildiko’s business succeeds” and “Eva’s business succeeds” independent?

Ildiko and Eva loans are “group loans”. Each person liable for (responsible for) their own loan and also the loan of the other. If Ildiko’s business succeeds and Eva’s fails, Ildiko must repay Eva’s loan in addition to repaying her own. If Eva’s business succeeds and Ildiko’s fails, Eva must repay Ildiko’s in addition to her own. If both businesses fail, then the group defaults on both loans. If both businesses succeed, Ildiko and Eva each repay their own loan.

Define event A to be “the microfinance company gets repaid on both loans”. Give the set of basic outcomes belonging to A. What is P(A)?

Answer 1

let event Ildiko's and Eva business success are I and E

1)The probability of only Eva succeeding is =P(E)-P(E n I)=0.65-0.55 =0.1

2)  probability that at least one of them succeeds is =P(E u I)=P(E)+P(I)-P(E n I)=0.75+0.65-0.55=0.85

3)probability that non of them succeeds is =1-P(E u I) =1-0.85 =0.15

4) as P(E)*P(I)=0.75*0.65=0.4875 wich is not equal to P(E n I)=0.55 ; hence  events “Ildiko’s business succeeds” and “Eva’s business succeeds” are not independent

5)set of elements of A are ; Eva business succeeds and  Ildiko’s fails ; Ildiko’s business succeeds and  Eva fails ; both business succeeds

P(A)=P(rpaid on both loans) =P(at least one succeed)=P(at least one succeed)=P(E u I)=0.85