Probability problem- Please Please help!

[Anonymous]

Two balls, each equally likely to be colored either red or blue, are put in an urn. At each stage one of the balls is randomly chosen, its color is noted, and it is returned to the urn. if the first two balls chosen are colored red, what is the probability that

a) both balls in the urn are colored red;

b) the next ball chosen will be red?

[torken]

each ball has a probability of 50% of being chosen, or 1/2.

since its replaced, the stages are independant.

a)

1/2 * 1/2 = 1/4 or 25% chance that both are red.

b)

Trick question, relates to the gambler's fallacy. The stages are independent, so the answer is 50%. It doesn't matter if you choose red a million times in a row, the probability of the next one being red is always 50%.

[Asker]

a) asks about the probability that both balls in the urn are red, not the probability to pick two red balls.

[torken]

I see.

Well then each ball has a 50% chance to be red, and the color of the other ball does not change that, its still independent. If there are two balls in the urn, then 50% * 50% is still 25%.

I don't think your choosing of the balls will affect that probability, since you are returning them.

[AllDay]

1/2 * 1/2 = 1/4

and since it the balls get placed back inside the urn its 1/2.

Meaning its independent of anything else

if it wasn't placed back inside then it would be dependent.

Any time its one turn its always (amount of picks) / (how many balls or cards are there)