Question

in a standard deck there are 52 cards. 26 of the cards are black, 26 of the cards are red. there are 4 suits: spades (black), clubs (black), hearts (red), and diamonds (red). there are 13 cards of each suit. the 13 cards range from 2, 3, 4, ... 10, j, q, k, a (refer to your notes) 11. if one card is drawn at random what is the probability that it is a spade? 12. if one card is drawn at random what is the probability that it is less than 5? 13. if one card is drawn at random what is the probability that it is not less than 5? 14. if one card is drawn at random what is the probability that it is a red king? 15. if one card is drawn at random what is the probability that it is a black heart?

Explanation:

Question 11

Step1: Identify total and favorable outcomes

Total cards: \( 52 \). Spades (favorable): \( 13 \) (1 suit, 13 cards each).

Step2: Calculate probability

Probability \( P = \frac{\text{Favorable}}{\text{Total}} = \frac{13}{52} \). Simplify: \( \frac{13 \div 13}{52 \div 13} = \frac{1}{4} \).

Step1: Determine cards less than 5 per suit

Cards less than 5: 2, 3, 4 (3 values) + A? Wait, the problem says "less than 5". So 2, 3, 4: 3 numbers? Wait, no—wait, the card values: 2,3,4, and A? Wait, no, "less than 5" as numbers: 2,3,4 (since 5 is not less than 5). Wait, but A is often considered as 1, which is less than 5? Wait[SSE onError error]

Answer:

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

Question 12