Question

1. a card is drawn from a standard deck of cards. find each probability.

a) ( p(\text{club}) )
b) ( p(\text{red card}) )
c) ( p(\text{not a heart}) )

Explanation:

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

Step 1: Recall deck composition

A standard deck has 52 cards. Clubs are one of 4 suits, each with 13 cards. So, number of clubs \( n(\text{club}) = 13 \), total cards \( N = 52 \).

Step 2: Apply probability formula

Probability \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \), so \( P(\text{club}) = \frac{13}{52} \).

Step 3: Simplify the fraction

\( \frac{13}{52} = \frac{1}{4} \).

Part (b): \( P(\text{red card}) \)

Step 1: Determine red card count

Red cards are hearts and diamonds, 2 suits with 13 cards each. So, number of red cards \( n(\text{red}) = 13 + 13 = 26 \), total cards \( N = 52 \).

Step 2: Calculate probability

Using \( P = \frac{n}{N} \), \( P(\text{red card}) = \frac{26}{52} \).

Step 3: Simplify

\( \frac{26}{52} = \frac{1}{2} \).

Part (c): \( P(\text{not a heart}) \)

Step 1: Find non - heart cards

Total cards \( N = 52 \), number of hearts \( n(\text{heart}) = 13 \). So, number of non - heart cards \( n(\text{not heart}) = 52 - 13 = 39 \).

Step 2: Compute probability

Using \( P = \frac{n}{N} \), \( P(\text{not a heart}) = \frac{39}{52} \).

Step 3: Simplify

\( \frac{39}{52} = \frac{3}{4} \).

Answer:

s:
a) \( \boldsymbol{\frac{1}{4}} \)

b) \( \boldsymbol{\frac{1}{2}} \)

c) \( \boldsymbol{\frac{3}{4}} \)