A draws two cards at random from a pack of 52 cards. After returning them to the pack and shuffling it, B draws two cards at random. The probability that their draws contain exactly one common card is:

$\frac{50}{663}$

Total number of ways = ${^{52}C}_2×{^{52}C}_2$

Total number of favourable ways = ${^{52}C}_2×{^{2}C}_1×{^{50}C}_1$