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
2671
A box contains 3 defective and 7 good light bulbs. If one bulb is drawn, what is the probability it is good?
Answer:
7/10
Step 1: Total bulbs = 3 + 7 = 10. Step 2: Favorable outcomes (good bulbs) = 7. Step 3: Probability = Favorable / Total = 7/10.
2672
A student guesses on 4 multiple-choice questions, each with 4 options. What is the probability of getting all correct by guessing?
Answer:
1/256
Step 1: Probability of getting one specific question right by guessing = 1/4. Step 2: The questions are independent. Step 3: Combined probability = (1/4)⁴ = 1/256.
2673
A student guesses on 3 true/false questions. What is the probability of getting all of them correct?
Answer:
1/8
Step 1: The probability of guessing one correct T/F answer is 1/2. Step 2: Guessing on each question is an independent event. Step 3: Probability = (1/2) × (1/2) × (1/2) = 1/8.
2674
Two coins and one die are tossed. Find the probability of getting exactly two Heads and an Even number.
Answer:
1/8
Step 1: The events (coins and die) are independent. P(Exactly 2 Heads with 2 coins) = 1/4. Step 2: P(Even number on a die) = 3/6 = 1/2. Step 3: Combined probability = (1/4) × (1/2) = 1/8.
2675
A coin and a die are tossed simultaneously. What is the probability of getting a Head and a 6?
Answer:
1/12
Step 1: The events are independent. P(Head) = 1/2. Step 2: P(Rolling a 6) = 1/6. Step 3: Combined probability = P(Head) × P(6) = (1/2) × (1/6) = 1/12.
2676
What is the probability of a sure (certain) event?
Answer:
1
Step 1: A sure event is one that will definitely happen. Step 2: Every possible outcome is a favorable outcome. Favorable outcomes = Total outcomes. Step 3: Hence, Probability = Total / Total = 1.
2677
If events A and B are independent with P(A) = 0.3 and P(B) = 0.6, find P(A or B).
Answer:
0.72
Step 1: Since they are independent, P(A and B) = P(A) × P(B) = 0.3 × 0.6 = 0.18. Step 2: Apply the addition rule: P(A or B) = P(A) + P(B) - P(A and B). Step 3: 0.3 + 0.6 - 0.18 = 0.90 - 0.18 = 0.72.
2678
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.
2679
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.
2680
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.