Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of the number of aces obtained in the two drawn cards. Then P(X=1) + P(X=2) equals?

The probability of drawing an ace in a single draw is 4/52 = 1/13. The probability of not drawing an ace is 1 - 1/13 = 12/13.

P(X=1) is the probability of drawing exactly one ace in two draws. This can happen in two ways:

1. Ace in the first draw, no ace in the second draw: (1/13) * (12/13) = 12/169
2. No ace in the first draw, ace in the second draw: (12/13) * (1/13) = 12/169

Therefore, P(X=1) = 12/169 + 12/169 = 24/169.

P(X=2) is the probability of drawing two aces in two draws:

P(X=2) = (1/13) * (1/13) = 1/169

Therefore, P(X=1) + P(X=2) = 24/169 + 1/169 = 25/169.

The correct option is B, 25/169.