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
2711
A bag contains 5 yellow and 4 pink balls. Two balls are drawn at random. What is the probability they are of different colors?
Answer:
5/9
Step 1: 'Different colors' is the complement of 'same color'. Step 2: The probability of same color is 4/9. Step 3: Probability = 1 - 4/9 = 5/9.
2712
A bag contains 5 yellow and 4 pink balls. Two balls are drawn at random. What is the probability they are of the same color?
Answer:
4/9
Step 1: Total balls = 9. We need P(Both Yellow) OR P(Both Pink). Step 2: P(YY) = (5/9) × (4/8) = 20/72. P(PP) = (4/9) × (3/8) = 12/72. Step 3: Add probabilities: 20/72 + 12/72 = 32/72 = 4/9.
2713
An urn contains 6 white and 4 black balls. If 3 balls are drawn at random without replacement, what is the probability they are all white?
Answer:
1/6
Step 1: Total balls = 10. Draw 1: P(W) = 6/10. Draw 2: P(W) = 5/9. Draw 3: P(W) = 4/8. Step 2: Multiply probabilities: (6/10) × (5/9) × (4/8). Step 3: (3/5) × (5/9) × (1/2) = (3/9) × (1/2) = (1/3) × (1/2) = 1/6.
2714
Bag A has 3 red and 2 blue balls. Bag B has 2 red and 4 blue balls. A bag is chosen at random, and a ball is drawn. What is the probability it is red?
Answer:
Both A and B
Step 1: Probability of picking Bag A = 1/2, Bag B = 1/2. Step 2: P(Red) = P(Bag A)×P(Red|A) + P(Bag B)×P(Red|B) = (1/2)×(3/5) + (1/2)×(2/6). Step 3: = 3/10 + 1/6 = 9/30 + 5/30 = 14/30, which simplifies to 7/15. Both A and B represent the same value.
2715
From a bag of 3 red, 4 blue, and 5 green marbles, two are drawn without replacement. What is the probability both are blue?
Answer:
1/11
Step 1: Total marbles = 12. P(First Blue) = 4/12 = 1/3. Step 2: Remaining total = 11, remaining blue = 3. P(Second Blue) = 3/11. Step 3: Probability = (1/3) × (3/11) = 1/11.
2716
A bag contains 3 red, 4 blue, and 5 green marbles. What is the probability of drawing a red or a blue marble in one draw?
Answer:
7/12
Step 1: Total marbles = 3 + 4 + 5 = 12. Step 2: The events are mutually exclusive. Favorable outcomes = (3 red) + (4 blue) = 7. Step 3: Probability = 7/12.
2717
A box contains 4 white and 5 black balls. Two balls are drawn with replacement. Probability of getting first white and second black is:
Answer:
20/81
Step 1: Events are independent due to replacement. Step 2: P(First White) = 4/9. P(Second Black) = 5/9. Step 3: Combined probability = (4/9) × (5/9) = 20/81.
2718
A box contains 4 white and 5 black balls. If two balls are drawn WITH replacement, what is the probability they are both white?
Answer:
16/81
Step 1: Total balls = 9. With replacement, the events are independent. P(First White) = 4/9. Step 2: P(Second White) = 4/9. Step 3: Combined probability = (4/9) × (4/9) = 16/81.
2719
A bag has 5 red and 3 green balls. Two balls are drawn without replacement. Find the probability of getting one red and one green ball.
Answer:
15/28
Step 1: Total balls = 8. There are two ways to get one of each: (Red then Green) OR (Green then Red). Step 2: P(RG) = (5/8) × (3/7) = 15/56. P(GR) = (3/8) × (5/7) = 15/56. Step 3: Total probability = 15/56 + 15/56 = 30/56 = 15/28.
2720
From a bag of 5 red and 3 green balls, two balls are drawn without replacement. What is the probability both are green?
Answer:
3/28
Step 1: Total balls = 8. P(First Green) = 3/8. Step 2: Remaining total = 7, remaining green = 2. P(Second Green) = 2/7. Step 3: Combined probability = (3/8) × (2/7) = 6/56 = 3/28.