A card is chosen randomly from a pack of playing cards. The probability that it is a black king or queen of heart or jack is

$\frac{7}{52}$

Let A, B, C are the events of choosing a black king, a queen of heart and a jack respectively.

$∴ P(A)=\frac{2}{52}, P(B) = \frac{1}{52}, P(C)=\frac{4}{52}$

These are mutually exclusive events, $∴ P(A ∪ B∪ C)=\frac{2}{52}+\frac{1}{52}+\frac{4}{52}=\frac{7}{52}.$