Question

a card is drawn from a well-shuffled deck of 52 cards. find the probability that the card is a red card or an 8. the probability is \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Recall the formula for probability of union

The formula for \( P(A \cup B) \) is \( P(A) + P(B) - P(A \cap B) \), where \( A \) is the event of drawing a red card and \( B \) is the event of drawing an 8.

Step2: Find \( P(A) \)

There are 26 red cards in a deck of 52. So \( P(A)=\frac{26}{52}=\frac{1}{2} \).

Step3: Find \( P(B) \)

There are 4 eights in a deck of 52. So \( P(B)=\frac{4}{52}=\frac{1}{13} \).

Step4: Find \( P(A \cap B) \)

The red eights are 2 (one in hearts, one in diamonds). So \( P(A \cap B)=\frac{2}{52}=\frac{1}{26} \).

Step5: Calculate \( P(A \cup B) \)

Substitute into the formula: \( P(A \cup B)=\frac{26}{52}+\frac{4}{52}-\frac{2}{52}=\frac{26 + 4 - 2}{52}=\frac{28}{52}=\frac{7}{13} \).

Answer:

\(\frac{7}{13}\)