Question

ne is a table showing all 52 cards in a standard deck. suppose one card is drawn at random from a standard deck. answer each part. write your answers as fractions in simplest form. (a) what is the probability that the card drawn is a red card? (b) what is the probability that the card drawn is a five? (c) what is the probability that the card drawn is a red card and a five?

Explanation:

Part (a)

Step1: Identify total and red cards

Total cards in a standard deck: \( 52 \).
Red cards: Hearts (13) + Diamonds (13) = \( 26 \).

Step2: Calculate probability

Probability \( = \frac{\text{Number of red cards}}{\text{Total cards}} = \frac{26}{52} \).
Simplify: \( \frac{26 \div 26}{52 \div 26} = \frac{1}{2} \).

Step1: Identify total and fives

Total cards: \( 52 \).
Number of fives: 4 (Hearts, Diamonds, Spades, Clubs).

Step2: Calculate probability

Probability \( = \frac{\text{Number of fives}}{\text{Total cards}} = \frac{4}{52} \).
Simplify: \( \frac{4 \div 4}{52 \div 4} = \frac{1}{13} \).

Step1: Identify red fives

Red suits: Hearts, Diamonds. So red fives: 2 (Heart 5, Diamond 5).
Total cards: \( 52 \).

Step2: Calculate probability

Probability \( = \frac{\text{Number of red fives}}{\text{Total cards}} = \frac{2}{52} \).
Simplify: \( \frac{2 \div 2}{52 \div 2} = \frac{1}{26} \).

Answer:

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

Part (b)