Although weekly events of NASDAQ returns are independent on each other, there's strong dependence on time. From my stats class I figured there many answers to your question depending which time series analysis we would perform... where did you get this question - the one is guaranteed to be out of my study scope for GMAT.

One way, though very primitive, I would approach this question by having 56 positive returns within 100 replication series. Out of 10 replications then I have 5.6 success rate, which means that the probability I have 4 positive within the next 10 weeks is very high -a)
b) could be resolved the same way, actually the one is just E (expected-average) for all data

further, various ways could be applied here, but we are missing data for some methods-exponential average

Utkarsh86 wrote:5. The weekly NASDAQ return was positive 56% of the time through January 2011. Assuming a random process with this probability, with returns independent from week to week,

a. What is the probability that returns will be positive in exactly 4 out of the next 10 weeks?
b. How likely is it that there will be positive returns in more than 30 of the next 50 weeks?

All help is appreciated

for part (i) is it 10c4 / 2^10 ??? (assuming nasdaq either increases or decreases in a given week - ignoring the remains constant from one week to another scenaro)
taking the third scenario into consideration i.e. it remains constant from one week to another, i think it should be 10C4 / 3^10

what's th OA?

a) success rate = 56/100

How to get exactly 4 out of 10 sucess rate = (4/10)(56/100) = 28/125