Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
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
71
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.
72
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.
73
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.
74
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.
75
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.
76
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.
77
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.
78
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.
79
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.
80
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.