Marbles in urn: probability of drawing homogeneous sample An urn has half red and half white marbles. The probability of getting all red or all white in 4 draws is 12.5% and the probability of getting all white or all red in 7 draws is 1.56%. How does one calculate these percentages without knowing the actual numbers of red and white marbles in the urn? 
 A: $P({\rm red}) = 0.50$
$P({\rm white}) = 0.50$
As @Whuber said, as long as the red/white ball is replaced after pulling one out (i.e. the experiment is done with replacement), then the probabilities of consecutive red/white pulls are 
$P({\rm red\ red\ red\ red}) = (0.50)(0.50)(0.50)(0.50) = 0.0625$
$P({\rm white\ white\ white\ white}) = (0.50)(0.50)(0.50)(0.50) = 0.0625$
So it actually looks like you're asking about 3 straight pulls of red or white, not 4.
How many marbles are in the actual urn is irrelevant.  It only matters what the probability of  red or white is on the current pull.  If there are 30 white and 30 red or 30,000 white and 30,000 red balls in the urn, it's still 50/50 of pulling a red or a white.
Again, this is only if you're replacing the ball after pulling it out.  If not, then the probability of pulling a red or white on the next pull is dependent on what you pulled out on the last pull.
Your second question looks like it's actually for 6 straight reds or 6 straight whites, not 7.
$P({\rm red\ red\ red\ red\ red\ red}) = (0.50)(0.50)(0.50)(0.50)(0.50)(0.50) = 0.015625$. 
The probability of 7 straight reds is half of that.
