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
2751
Two dice are rolled. What is the probability that both dice show a multiple of 3?
Answer:
1/9
Step 1: Total outcomes = 36. Multiples of 3 on a die are {3, 6}. Step 2: Favorable pairs are (3,3), (3,6), (6,3), (6,6). Total = 4. Step 3: Probability = 4/36 = 1/9.
2752
When two dice are thrown simultaneously, what is the probability that the sum is a prime number?
Answer:
5/12
Step 1: Total outcomes = 36. Prime sums possible are 2, 3, 5, 7, 11. Step 2: Number of ways for each: sum 2 (1), sum 3 (2), sum 5 (4), sum 7 (6), sum 11 (2). Total ways = 1 + 2 + 4 + 6 + 2 = 15. Step 3: Probability = 15/36 = 5/12.
2753
Two dice are tossed. What is the probability of getting a doublet (same number on both dice)?
Answer:
1/6
Step 1: Total outcomes = 36. Step 2: The doublets are (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). Favorable outcomes = 6. Step 3: Probability = 6/36 = 1/6.
2754
What is the probability of getting a sum greater than 9 when rolling two dice?
Answer:
1/6
Step 1: Total outcomes = 36. Step 2: A sum greater than 9 means sums of 10, 11, or 12. Favorable outcomes: (4,6), (5,5), (6,4), (5,6), (6,5), (6,6). Total = 6. Step 3: Probability = 6/36 = 1/6.
2755
If two dice are thrown, find the probability that the sum of the faces equals 8.
Answer:
5/36
Step 1: Total outcomes = 36. Step 2: Favorable outcomes for a sum of 8 are (2,6), (3,5), (4,4), (5,3), (6,2). Total = 5. Step 3: Probability = 5/36.
2756
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Answer:
1/6
Step 1: Total outcomes when two dice are rolled = 6 × 6 = 36. Step 2: Outcomes yielding a sum of 7 are (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Favorable outcomes = 6. Step 3: Probability = 6/36 = 1/6.
2757
What is the probability of rolling a number greater than 4 on a fair die?
Answer:
1/3
Step 1: Total possible outcomes = 6. Step 2: Numbers greater than 4 are {5, 6}. Favorable outcomes = 2. Step 3: Probability = 2/6 = 1/3.
2758
When a single die is rolled, what is the probability of getting a prime number?
Answer:
1/2
Step 1: Total outcomes = 6. Step 2: The prime numbers on a die are {2, 3, 5}. Favorable outcomes = 3. (Note: 1 is not a prime number). Step 3: Probability = 3/6 = 1/2.
2759
What is the probability of rolling an even number on a standard six-sided die?
Answer:
1/2
Step 1: The sample space is {1, 2, 3, 4, 5, 6}. Total outcomes = 6. Step 2: The even numbers are {2, 4, 6}. Favorable outcomes = 3. Step 3: Probability = 3/6 = 1/2.
2760
A biased coin has a 60% chance of landing on heads. If tossed twice, what is the probability of getting two heads?
Answer:
0.36
Step 1: The probability of heads P(H) = 0.6. Step 2: The tosses are independent events. Probability of two heads = P(H) × P(H). Step 3: 0.6 × 0.6 = 0.36.