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
31
Given P(A and B) = 0.2 and P(B) = 0.5, what is the conditional probability P(A|B)?
Answer:
0.4
Step 1: The formula for conditional probability is P(A|B) = P(A and B) / P(B). Step 2: Substitute the known values into the formula. Step 3: P(A|B) = 0.2 / 0.5 = 2/5 = 0.4.
32
If the probability of an event A occurring is 0.2, what is the probability of event A NOT occurring?
Answer:
0.8
Step 1: The sum of probabilities of an event happening and not happening is 1. P(A) + P(Not A) = 1. Step 2: P(Not A) = 1 - P(A). Step 3: 1 - 0.2 = 0.8.
33
The odds against an event are 5:4. What is the probability of the event occurring?
Answer:
4/9
Step 1: Odds against = Unfavorable : Favorable = 5:4. Step 2: This means there are 4 favorable outcomes and 5 unfavorable. Total outcomes = 9. Step 3: Probability of occurring = Favorable / Total = 4/9.
34
The odds in favor of an event are 3:2. What is the probability of the event occurring?
Answer:
3/5
Step 1: Odds in favor = Favorable : Unfavorable = 3:2. Step 2: Total possible outcomes = Favorable + Unfavorable = 3 + 2 = 5. Step 3: Probability = Favorable / Total = 3/5.
35
If P(A) = 0.6, P(B) = 0.5, and P(A and B) = 0.3, find P(A or B).
Answer:
0.8
Step 1: Use the general addition rule for probability. Step 2: P(A or B) = P(A) + P(B) - P(A and B). Step 3: P(A or B) = 0.6 + 0.5 - 0.3 = 1.1 - 0.3 = 0.8.
36
Events A and B are independent. If P(A) = 0.5 and P(B) = 0.4, find P(A and B).
Answer:
0.20
Step 1: For independent events, the probability of both occurring is the product of their individual probabilities. Step 2: Formula: P(A and B) = P(A) × P(B). Step 3: 0.5 × 0.4 = 0.20.
37
Events A and B are mutually exclusive. If P(A) = 0.4 and P(B) = 0.5, what is P(A or B)?
Answer:
0.90
Step 1: Mutually exclusive events cannot happen at the same time, so P(A and B) = 0. Step 2: Use the addition rule: P(A or B) = P(A) + P(B) - P(A and B). Step 3: 0.4 + 0.5 - 0 = 0.90.
38
If the letters of the word 'RANDOM' are arranged, what is the probability the arrangement ends with 'M'?
Answer:
1/6
Step 1: The total number of arrangements of the 6 distinct letters is 6!. Step 2: Fix 'M' at the end. The remaining 5 letters can be arranged in 5! ways. Step 3: Probability = 5! / 6! = 1/6.
39
A letter is randomly selected from the word 'VOWEL'. What is the probability that it is the letter 'V'?
Answer:
1/5
Step 1: The word 'VOWEL' has 5 letters. Step 2: The letter 'V' occurs 1 time. Step 3: Probability = 1/5.
40
A PIN consists of 4 digits (0-9). What is the probability that all 4 digits are the same?
Answer:
Both A and B
Step 1: Total possible PINs = 10⁴ = 10,000. Step 2: PINs with identical digits are 0000, 1111, ..., 9999 (Total 10). Step 3: Probability = 10/10000, which simplifies to 1/1000. Both A and B are correct.