Question

for the experiment of drawing a single card from a standard 52 - card deck, find (a) the probability of the following event, and (b) the odds in favor of the following event. spade or face card (a) the probability that the card is either a spade or a face card is (simplify your answer.)

Explanation:

Step1: Calculate the number of spades, face cards, and their intersection

• Number of spades (\(n(S)\)): A standard deck has 13 spades.
• Number of face cards (\(n(F)\)): There are 12 face cards (4 Jacks, 4 Queens, 4 Kings).
• Number of cards that are both spades and face cards (\(n(S\cap F)\)): There are 3 face - cards in spades (Jack, Queen, King of spades).

Step2: Use the formula \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

• \(P(S)=\frac{13}{52}\), \(P(F)=\frac{12}{52}\), \(P(S\cap F)=\frac{3}{52}\)
• \(P(S\cup F)=\frac{13 + 12- 3}{52}=\frac{22}{52}=\frac{11}{26}\)

Answer:

\(\frac{11}{26}\)