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
2741
If a card is drawn from a standard 52-card deck, what is the probability that it is a face card?
Answer:
3/13
Step 1: Total cards = 52. Step 2: Face cards are Jacks, Queens, and Kings. There are 3 per suit, and 4 suits, giving 3 × 4 = 12 face cards. Step 3: Probability = 12/52 = 3/13.
2742
One card is drawn randomly from a standard deck. What is the probability of drawing a Red Queen?
Answer:
1/26
Step 1: Total cards = 52. Step 2: There are 2 red Queens (Hearts and Diamonds). Favorable outcomes = 2. Step 3: Probability = 2/52 = 1/26.
2743
A card is drawn from a standard deck of 52 cards. What is the probability that the card is a Spade?
Answer:
1/4
Step 1: Total outcomes = 52. Step 2: There are 13 spades in a deck. Favorable outcomes = 13. Step 3: Probability = 13/52 = 1/4.
2744
From a well-shuffled deck of 52 cards, one card is drawn. What is the probability that it is a King?
Answer:
1/13
Step 1: Total number of cards = 52. Step 2: There are 4 Kings in a standard deck. Favorable outcomes = 4. Step 3: Probability = 4/52 = 1/13.
2745
If three dice are rolled, what is the probability that the sum of the upward faces is 18?
Answer:
1/216
Step 1: Total outcomes = 216. Step 2: The only combination to achieve a sum of 18 is (6, 6, 6). Favorable outcomes = 1. Step 3: Probability = 1/216.
2746
Three standard dice are rolled. What is the probability that the sum of the numbers is 3?
Answer:
1/216
Step 1: Total outcomes for 3 dice = 6 × 6 × 6 = 216. Step 2: The only way to get a sum of 3 is (1, 1, 1). Favorable outcomes = 1. Step 3: Probability = 1/216.
2747
Two dice are rolled. What is the probability that the product of the numbers is odd?
Answer:
1/4
Step 1: For the product to be odd, both numbers must be odd. Step 2: The probability of getting an odd number on one die is 3/6 = 1/2. Step 3: Since rolls are independent, P(Odd AND Odd) = (1/2) × (1/2) = 1/4.
2748
What is the probability that the product of the numbers obtained by rolling two fair dice is 12?
Answer:
1/9
Step 1: Total outcomes = 36. Step 2: Favorable pairs yielding a product of 12 are (2,6), (3,4), (4,3), (6,2). Total = 4. Step 3: Probability = 4/36 = 1/9.
2749
Two dice are rolled. What is the probability that the sum of the numbers is less than or equal to 4?
Answer:
1/6
Step 1: Total outcomes = 36. Step 2: Sums <= 4 are 2, 3, or 4. Favorable outcomes: (1,1), (1,2), (2,1), (1,3), (2,2), (3,1). Total = 6. Step 3: Probability = 6/36 = 1/6.
2750
If two fair dice are rolled, find the probability that the sum is exactly 12.
Answer:
1/36
Step 1: Total outcomes = 36. Step 2: The only way to get a sum of 12 is (6,6). Favorable outcomes = 1. Step 3: Probability = 1/36.