Probability Problem Solving

[theachiever]

On 30 percent of days, Peter the Parrot predicts that the stock market will go up. On 43percent of days, the market actually goes up. On 12 percent of days, Peter predicts that the market will go up and it does. If we pick a day at random, what is the probability that:
"¢Peter will predict that the market will go up, or it will actually go up, or both?
"¢The market will actually go up given that Peter has predicted it will?
"¢Does the Stock market moves up independently of Peter's Prediction?


Experts please help

[Matt@VeritasPrep]

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.

[theachiever]

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.

[jitsy]

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