a card is drawn from a standard deck of 52 playing cards. find the probability that the card is a jack or a…

Explanation:

Step1: Define event probabilities

Let $A$ be the event of drawing a Jack and $B$ be the event of drawing a black - card. There are 4 Jacks in a deck of 52 cards, so $P(A)=\frac{4}{52}$. There are 26 black cards in a deck of 52 cards, so $P(B)=\frac{26}{52}$. There are 2 black Jacks (Jack of spades and Jack of clubs), so $P(A\cap B)=\frac{2}{52}$.

Step2: Use the addition rule of probability

The addition rule for two events $A$ and $B$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Substitute the values: $P(A\cup B)=\frac{4}{52}+\frac{26}{52}-\frac{2}{52}$.

Step3: Calculate the result

$P(A\cup B)=\frac{4 + 26-2}{52}=\frac{28}{52}=\frac{7}{13}$.

Answer:

$\frac{7}{13}$