Question

what is the probability of drawing each of the following cards from a standard playing deck? see the entry \playing cards\ in the glossary to learn what playing cards are included in a deck. homework help a. ( p(\text{jack}) ) b. ( p(\text{spade}) ) c. ( p(\text{jack of spades}) ) d. ( p(\text{not spade}) )

Explanation:

Part a: \( P(\text{Jack}) \)

Step 1: Determine total and favorable outcomes

A standard deck has 52 cards. There are 4 Jacks (one per suit: hearts, diamonds, clubs, spades).

Step 2: Calculate probability

Probability is \( \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} \), so \( P(\text{Jack}) = \frac{4}{52} \). Simplify by dividing numerator and denominator by 4: \( \frac{4\div4}{52\div4} = \frac{1}{13} \).

Part b: \( P(\text{spade}) \)

Step 1: Determine total and favorable outcomes

Total cards: 52. Number of spades: 13 (Ace to King of spades).

Step 2: Calculate probability

\( P(\text{spade}) = \frac{13}{52} \). Simplify by dividing numerator and denominator by 13: \( \frac{13\div13}{52\div13} = \frac{1}{4} \).

Part c: \( P(\text{Jack of spades}) \)

Step 1: Determine total and favorable outcomes

Total cards: 52. There is 1 Jack of spades.

Step 2: Calculate probability

\( P(\text{Jack of spades}) = \frac{1}{52} \).

Part d: \( P(\text{not spade}) \)

Answer:

s:
a. \( \frac{1}{13} \)

b. \( \frac{1}{4} \)

c. \( \frac{1}{52} \)

d. \( \frac{3}{4} \)