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
2721
An urn has 5 red and 3 green balls. If two balls are drawn randomly without replacement, find the probability that both are red.
Answer:
5/14
Step 1: Total balls = 8. P(First Red) = 5/8. Step 2: After drawing one red, 4 red and 3 green remain. Total = 7. P(Second Red) = 4/7. Step 3: Combined probability = (5/8) × (4/7) = 20/56 = 5/14.
2722
A bag contains 2 red, 3 blue, and 4 white balls. What is the probability of drawing a blue ball?
Answer:
1/3
Step 1: Total number of balls = 2 + 3 + 4 = 9. Step 2: Number of blue balls = 3. Step 3: Probability = 3/9, which simplifies to 1/3.
2723
An urn contains 4 green and 5 black marbles. If one marble is drawn, what is the probability it is NOT green?
Answer:
5/9
Step 1: Total marbles = 4 + 5 = 9. Step 2: The marbles that are NOT green are the black ones, which equal 5. Step 3: Probability = 5/9.
2724
A bag contains 3 red balls and 2 blue balls. What is the probability of drawing a red ball?
Answer:
3/5
Step 1: Total number of balls = 3 + 2 = 5. Step 2: Favorable outcomes (red balls) = 3. Step 3: Probability = Favorable / Total = 3/5.
2725
Two cards are drawn with replacement. What is the probability that the first is red and the second is black?
Answer:
1/4
Step 1: With replacement, events are independent. P(Red) = 26/52 = 1/2. Step 2: P(Black) on the second draw = 26/52 = 1/2. Step 3: Probability = (1/2) × (1/2) = 1/4.
2726
What is the probability of drawing a Jack, a Queen, or a King from a well-shuffled deck?
Answer:
3/13
Step 1: The events are mutually exclusive. Jacks = 4, Queens = 4, Kings = 4. Step 2: Total favorable cards = 12. Step 3: Probability = 12/52 = 3/13.
2727
A card is picked at random. What is the probability it is a spade or a diamond?
Answer:
1/2
Step 1: Spades and diamonds are mutually exclusive events. Spades = 13, Diamonds = 13. Step 2: Total favorable cards = 13 + 13 = 26. Step 3: Probability = 26/52 = 1/2.
2728
What is the probability of drawing a card with a prime number (2, 3, 5, or 7) from a standard deck?
Answer:
Both A and B
Step 1: Prime numbers on cards are 2, 3, 5, and 7. That's 4 cards per suit. Step 2: Total prime number cards = 4 × 4 = 16. Step 3: Probability = 16/52 = 4/13. Both A and B are correct.
2729
A card is drawn from a standard deck. What is the probability it is a number card from 2 to 10?
Answer:
Both A and B
Step 1: Cards numbered 2 through 10 total 9 cards per suit. Step 2: Across 4 suits, there are 9 × 4 = 36 such cards. Step 3: Probability = 36/52, which simplifies to 9/13. Both A and B are correct representations.
2730
If three cards are drawn sequentially without replacement, what is the probability that they are all Aces?
Answer:
1/5525
Step 1: P(First Ace) = 4/52. P(Second Ace) = 3/51. P(Third Ace) = 2/50. Step 2: Multiply them: (1/13) × (1/17) × (1/25). Step 3: (1 × 1 × 1) / (13 × 17 × 25) = 1 / (221 × 25) = 1/5525.