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
2701
If a two-digit number is chosen at random, find the probability that both its digits are the same.
Answer:
1/10
Step 1: Total two-digit numbers = 90. Step 2: Numbers with identical digits are 11, 22, 33, 44, 55, 66, 77, 88, 99. Total = 9. Step 3: Probability = 9/90 = 1/10.
2702
What is the probability that a randomly chosen two-digit number is a multiple of 10?
Answer:
1/10
Step 1: Total two-digit numbers = 90. Step 2: Multiples of 10 are 10, 20, 30, ..., 90. There are 9 such numbers. Step 3: Probability = 9/90 = 1/10.
2703
What is the probability that a randomly chosen two-digit positive integer has a sum of digits equal to 9?
Answer:
1/10
Step 1: Total two-digit numbers (10 to 99) = 90. Step 2: Numbers with sum 9: 18, 27, 36, 45, 54, 63, 72, 81, 90. Total = 9 outcomes. Step 3: Probability = 9/90 = 1/10.
2704
A number is picked from 1 to 20. Find the probability that it is divisible by both 4 and 6.
Answer:
1/20
Step 1: A number divisible by both 4 and 6 must be divisible by their LCM, which is 12. Step 2: Multiples of 12 between 1 and 20 is just 12 (1 outcome). Step 3: Probability = 1/20.
2705
A number is chosen from 1 to 50. What is the probability that it is a multiple of either 3 or 5?
Answer:
23/50
Step 1: Multiples of 3 = int(50/3) = 16. Multiples of 5 = int(50/5) = 10. Step 2: Multiples of both 3 and 5 (i.e., 15) = int(50/15) = 3. Step 3: Total favorable = 16 + 10 - 3 = 23. Probability = 23/50.
2706
If a number is selected at random from the integers 1 to 50, what is the probability that it is a multiple of 5?
Answer:
1/5
Step 1: Total numbers = 50. Step 2: Multiples of 5 up to 50 are 5, 10, ..., 50. There are 50/5 = 10 multiples. Step 3: Probability = 10/50 = 1/5.
2707
A number is chosen from 1 to 100. What is the probability that it is a perfect square?
Answer:
1/10
Step 1: Total numbers = 100. Step 2: Perfect squares from 1 to 100 are 1², 2², ..., 10² (1, 4, 9, 16, 25, 36, 49, 64, 81, 100). Total 10. Step 3: Probability = 10/100 = 1/10.
2708
A number is selected at random from the integers 1 to 20. Find the probability that it is a prime number.
Answer:
2/5
Step 1: Total numbers = 20. Step 2: Primes from 1 to 20 are 2, 3, 5, 7, 11, 13, 17, 19. (Total 8). Step 3: Probability = 8/20 = 2/5.
2709
A number is chosen at random from 1 to 10. What is the probability that it is an even number?
Answer:
1/2
Step 1: Total numbers = 10. Step 2: Even numbers from 1 to 10 are 2, 4, 6, 8, 10 (Total 5). Step 3: Probability = 5/10 = 1/2.
2710
A box has 7 red and 3 blue chips. What is the probability of drawing a blue chip?
Answer:
3/10
Step 1: Total chips = 7 + 3 = 10. Step 2: Favorable chips (blue) = 3. Step 3: Probability = Favorable / Total = 3/10.