All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
2731
Two cards are drawn from a deck without replacement. What is the probability that both are black?
Answer:
25/102
Step 1: Probability of first black card = 26/52 = 1/2. Step 2: Probability of second black card = 25/51. Step 3: Total probability = (1/2) × (25/51) = 25/102.
2732
Two cards are drawn sequentially WITH replacement. What is the probability that both are Aces?
Answer:
1/169
Step 1: With replacement, the events are independent. Probability of first Ace = 4/52 = 1/13. Step 2: Probability of second Ace = 4/52 = 1/13. Step 3: Combined probability = (1/13) × (1/13) = 1/169.
2733
What is the probability of drawing two Spades sequentially without replacement from a deck of 52 cards?
Answer:
1/17
Step 1: Probability of first Spade = 13/52 = 1/4. Step 2: Probability of second Spade = 12/51 = 4/17. Step 3: Combined probability = (1/4) × (4/17) = 1/17.
2734
Two cards are drawn without replacement. What is the probability of drawing one King and one Queen in that exact order?
Answer:
4/663
Step 1: Probability of the first card being a King = 4/52. Step 2: Probability of the second card being a Queen = 4/51. Step 3: Combined probability = (4/52) × (4/51) = (1/13) × (4/51) = 4/663.
2735
If two cards are drawn from a pack without replacement, what is the probability that both are red?
Answer:
25/102
Step 1: Probability of drawing the first red card = 26/52 = 1/2. Step 2: Probability of drawing the second red card = 25/51. Step 3: Combined probability = (1/2) × (25/51) = 25/102.
2736
Two cards are drawn sequentially without replacement from a standard deck. What is the probability that both are Kings?
Answer:
1/221
Step 1: Probability of first card being a King = 4/52 = 1/13. Step 2: Probability of second card being a King (without replacement) = 3/51 = 1/17. Step 3: Combined probability = (1/13) × (1/17) = 1/221.
2737
A card is drawn from a 52-card deck. What is the probability that it is neither a heart nor a king?
Answer:
9/13
Step 1: Total hearts = 13. Total kings = 4. Heart king is 1. P(Heart or King) = (13 + 4 - 1)/52 = 16/52 = 4/13. Step 2: 'Neither' is the complement of 'either'. Step 3: Probability = 1 - 4/13 = 9/13.
2738
What is the probability of drawing a card that is both red and a face card?
Answer:
3/26
Step 1: Total cards = 52. Step 2: The red suits are Hearts and Diamonds. Each has 3 face cards, making 6 red face cards. Step 3: Probability = 6/52 = 3/26.
2739
One card is drawn from a well-shuffled deck. Find the probability that the card is either black or a King.
Answer:
7/13
Step 1: Total black cards = 26. Total Kings = 4. Step 2: Black Kings (2) are counted twice, so favorable outcomes = 26 + 4 - 2 = 28. Step 3: Probability = 28/52 = 7/13.
2740
A card is drawn from a deck of 52 cards. What is the probability that it is NOT an Ace?
Answer:
12/13
Step 1: Probability of drawing an Ace is 4/52 = 1/13. Step 2: The probability of NOT drawing an Ace is the complement. Step 3: Probability = 1 - 1/13 = 12/13.