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
2691
Three boys and two girls sit in a row. What is the probability that the two girls sit together?
Answer:
2/5
Step 1: Total unrestricted arrangements of 5 people = 5! = 120. Step 2: Treat the 2 girls as one unit. Arrangements = 4! × 2! (internal arrangement) = 24 × 2 = 48. Step 3: Probability = 48 / 120 = 2/5.
2692
If the letters of the word 'APPLE' are arranged randomly, what is the probability that the two P's are together?
Answer:
2/5
Step 1: Total arrangements of 'APPLE' = 5! / 2! = 120 / 2 = 60. Step 2: Treat 'PP' as a single entity. Entities = (PP), A, L, E. Ways to arrange = 4! = 24. Step 3: Probability = Favorable / Total = 24 / 60 = 2/5.
2693
If a letter is chosen at random from the word 'MISSISSIPPI', find the probability that it is an 'S'.
Answer:
4/11
Step 1: Total letters in 'MISSISSIPPI' = 11. Step 2: The letter 'S' appears 4 times. Step 3: Probability = 4/11.
2694
A letter is chosen at random from the word 'MATHEMATICS'. What is the probability that it is an 'M'?
Answer:
2/11
Step 1: Count total letters in 'MATHEMATICS' = 11. Step 2: Count the occurrences of 'M', which is 2. Step 3: Probability = 2/11.
2695
If a letter is chosen at random from the English alphabet, what is the probability that it is a vowel?
Answer:
5/26
Step 1: Total letters in the English alphabet = 26. Step 2: Vowels are A, E, I, O, U (Total 5). Step 3: Probability = Favorable / Total = 5/26.
2696
If a month of the year is selected at random, what is the probability that it has exactly 31 days?
Answer:
7/12
Step 1: Total months in a year = 12. Step 2: Months with 31 days are Jan, Mar, May, Jul, Aug, Oct, Dec. Total = 7. Step 3: Probability = 7/12.
2697
What is the probability that a leap year contains 53 Sundays OR 53 Mondays?
Answer:
3/7
Step 1: P(53 Sundays) = 2/7. P(53 Mondays) = 2/7. Step 2: P(Both) = 1/7. Step 3: Using the addition rule: P(Sun OR Mon) = P(Sun) + P(Mon) - P(Both) = 2/7 + 2/7 - 1/7 = 3/7.
2698
What is the probability that a randomly chosen leap year contains both 53 Sundays AND 53 Mondays?
Answer:
1/7
Step 1: A leap year has 2 extra days. Step 2: The possible consecutive day pairs are 7. The only pair containing both Sunday and Monday is (Sunday, Monday). Step 3: There is 1 favorable outcome out of 7. Probability = 1/7.
2699
What is the probability that an ordinary (non-leap) year contains exactly 53 Mondays?
Answer:
1/7
Step 1: An ordinary year has 365 days, which is 52 weeks and 1 extra day. Step 2: The extra day can be any of the 7 days of the week. Step 3: For there to be 53 Mondays, the extra day must be a Monday. Probability = 1/7.
2700
What is the probability that a leap year, selected at random, will contain 53 Sundays?
Answer:
2/7
Step 1: A leap year has 366 days, which is 52 complete weeks (364 days) and 2 extra days. Step 2: The 2 extra days can be (Sun-Mon, Mon-Tue, Tue-Wed, Wed-Thu, Thu-Fri, Fri-Sat, Sat-Sun). There are 7 pairs. Step 3: Sundays appear in 2 pairs (Sat-Sun and Sun-Mon). Probability = 2/7.