The total number of sweets is 52 (13 red + 13 blue + 13 green + 13 yellow). We need to find the probability of selecting exactly 3 red sweets out of 7.

Using combinations, the number of ways to choose 3 red sweets from 13 is given by:

\(\binom{13}{3}\)

The number of ways to choose the remaining 4 sweets from the 39 non-red sweets is:

\(\binom{39}{4}\)

The total number of ways to choose 7 sweets from 52 is:

\(\binom{52}{7}\)

Thus, the probability is:

\(\frac{\binom{13}{3} \times \binom{39}{4}}{\binom{52}{7}}\)

Calculating these values:

\(\binom{13}{3} = 286\)

\(\binom{39}{4} = 82,251\)

\(\binom{52}{7} = 133,784,560\)

Therefore, the probability is:

\(\frac{286 \times 82,251}{133,784,560} \approx 0.176\)