Let's get our probabilities straight first.

PETER SAYS UP: 30%
PETER DOESN'T SAY UP: 70%

MARKET GOES UP: 43%
MARKET DOESN'T GO UP: 57%

So the odds of Peter saying up and the market going up should be 30% * 43% = 12.9%, assuming the two events are independent. What this problem implies, however, is that the events are NOT independent: the odds are different (12%) from the independent expectation (12.9%). (Maybe Peter is an oracle, like that German squid who correctly predicted all the World Cup and European Championship results, and the market fears his opinion. )

This sort of conditional probability is a little beyond the GMAT, however. I'm happy to explain it, but I'd say it's a waste of time - as far as I know, the GMAT doesn't assume you know how to do this.

Thanks Matt. I appreciate the help.I will be posting the solution in another method for all the qiuestions that I have posted.Please kindly let me know if I am right.

1)"¢Peter will predict that the market will go up, or it will actually go up, or both

P(a)=0.30
P(b)=0.43
P(A and B)=0.12

P(A or B)= P(a)+P(b)-P(A and b)
= 0.30+0.43-0.12=0.61

2."¢The market will actually go up given that Peter has predicted it will?

p(b/a)=P(B and A)/P(a)=0.12/0.30=0.40

3.Does the Stock market moves up independently of Peter's Prediction?

Since P(b) is not equal to p(b/a) events A and B are not independent.Hence stock markets do not move independently.

Please let me know if I am correct.

Agree with the first two answers but isn't the market movement independent of the prediction. How should one think about this particular question.