Question: 30. Two balls, each equally likely to be colored either red or blue, are put in an urn. At each stage one of the balls

30. 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 then 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?

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