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
2681
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.
2682
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.
2683
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.
2684
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.
2685
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.
2686
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.
2687
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.
2688
A password consists of 3 digits (0-9). What is the probability of guessing the correct password on the first try?
Answer:
1/1000
Step 1: Each digit can be anything from 0 to 9 (10 options). Total combinations = 10 × 10 × 10 = 1000. Step 2: There is only exactly 1 correct password. Step 3: Probability = 1/1000.
2689
Five books are placed randomly on a shelf. What is the probability that two specific books are placed next to each other?
Answer:
2/5
Step 1: Total arrangements of 5 books = 5! = 120. Step 2: Treat the two specific books as a single unit. We now arrange 4 units: 4! = 24 ways. The two books can swap places: 2! = 2. Total favorable = 24 × 2 = 48. Step 3: Probability = 48 / 120 = 2/5.
2690
Five people sit in a circle. What is the probability that two specific persons sit together?
Answer:
1/2
Step 1: Total circular permutations for 5 people = (5-1)! = 4! = 24. Step 2: Treat the two specific people as a single unit. Total units = 4. Circular permutations = (4-1)! = 3! = 6. Internal arrangements of the two = 2!. Favorable ways = 6 × 2 = 12. Step 3: Probability = 12 / 24 = 1/2.