SECTION F — Assertion and Reasoning Type Questions [1 Marks Each]
Directions: Each of the following questions consists of two statements, namely, Assertion (A) and Reason (R). Select the correct option from the choices given below:
- (a) Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
- (b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- (c) Assertion (A) is true, but Reason (R) is false.
- (d) Assertion (A) is false, but Reason (R) is true.
-
Q1. Assertion (A): When a fair coin is tossed once, the probability of getting a head is $\frac{1}{2}$.
Reason (R): The number of possible outcomes for a single coin toss is 2 (Head and Tail), and both outcomes are equally likely. -
Q2. Assertion (A): The probability of getting a number 7 on a single throw of a standard six-faced die is 0.
Reason (R): An event that cannot occur is called an impossible event, and its probability is always 0. -
Q3. Assertion (A): If $E$ is an event, then $P(E) + P(\text{not } E) = 1$.
Reason (R): The sum of the probabilities of all elementary events of an experiment is equal to 1. -
Q4. Assertion (A): The probability of an event can be equal to $1.5$.
Reason (R): The probability of any event $E$ is a fraction or decimal that always lies in the range $0 \le P(E) \le 1$. -
Q5. Assertion (A): If the probability of winning a game is $0.7$, then the probability of losing the game is $0.3$.
Reason (R): Winning and losing are complementary events whose probabilities add up to 1. -
Q6. Assertion (A): From a well-shuffled deck of 52 playing cards, the probability of drawing a red face card is $\frac{3}{26}$.
Reason (R): There are 6 red face cards in a standard deck of 52 cards (2 jacks, 2 queens, and 2 kings). -
Q7. Assertion (A): When two dice are thrown simultaneously, the maximum sum of the numbers appearing on them is 12.
Reason (R): The highest number on a standard die face is 6, so $6 + 6 = 12$. -
Q8. Assertion (A): In a single throw of a die, the probability of getting a prime number is $\frac{1}{2}$.
Reason (R): The prime numbers on a standard die are 2, 3, and 5, giving a total of 3 favorable outcomes out of 6 possible outcomes. -
Q9. Assertion (A): When two coins are tossed simultaneously, the probability of getting at least one head is $\frac{3}{4}$.
Reason (R): The sample space consists of 4 outcomes: $\{HH, HT, TH, TT\}$, out of which 3 outcomes contain at least one head. -
Q10. Assertion (A): A box contains 90 discs numbered 1 to 90. The probability of drawing a disc bearing a two-digit number is $\frac{9}{10}$.
Reason (R): There are 81 two-digit numbers from 1 to 90. -
Q11. Assertion (A): The probability of selecting a day of the week that starts with the letter 'M' (Monday) from a week is $\frac{1}{7}$.
Reason (R): A sure event has a probability of 1. -
Q12. Assertion (A): The probability that a leap year will have 53 Sundays is $\frac{2}{7}$.
Reason (R): A leap year has 366 days, which consists of 52 full weeks and 2 extra days. These 2 extra days can form 7 possible pairs. -
Q13. Assertion (A): The probability of drawing a king from a well-shuffled deck of 52 cards is $\frac{1}{13}$.
Reason (R): There are 4 kings in a standard deck of 52 cards. -
Q14. Assertion (A): The probability of an event can take a negative value like $-0.05$ under complex statistical conditions.
Reason (R): Probability values are strictly non-negative real numbers bounded between 0 and 1 inclusive. -
Q15. Assertion (A): A bag contains 3 red and 5 black balls. The probability of drawing a black ball is $\frac{5}{8}$.
Reason (R): Probability is calculated as the ratio of the number of favorable outcomes to the total number of outcomes. -
Q16. Assertion (A): A spinner is numbered 1 to 8. The probability of pointing to a prime number is $\frac{1}{2}$.
Reason (R): The prime numbers between 1 and 8 are 2, 3, 5, and 7, totaling 4 favorable outcomes. -
Q17. Assertion (A): The probability that a randomly chosen non-leap year has 53 Sundays is $\frac{1}{7}$.
Reason (R): A non-leap year has 365 days, yielding 52 weeks and 1 extra day, which can be any day of the week with equal likelihood. -
Q18. Assertion (A): In a single throw of a fair die, the probability of getting a composite number is $\frac{1}{3}$.
Reason (R): The composite numbers on a die are 4 and 6, making 2 favorable outcomes out of 6. -
Q19. Assertion (A): If the queen of hearts is removed from a deck of 52 cards, the probability of drawing a heart card changes from $\frac{1}{4}$ to $\frac{12}{51}$.
Reason (R): Removing a card reduces both the total number of cards in the deck and the count of that specific suit. -
Q20. Assertion (A): The sum of the probabilities of all the elementary events of an experiment is 1.
Reason (R): An elementary event has only one outcome, and the totality of all elementary events covers the complete sample space of the random experiment.
Academic Repository Disclaimer & எச்சரிக்கை அறிவிப்பு :
English: These model solutions are structured to global academic standards for self-assessment and practice purposes. Students are advised to verify with official textbooks for board examinations.
தமிழ்: இந்த மாதிரி கணிதத் தீர்வுகள் மாணவர்களின் சுய கற்றல் மற்றும் பயிற்சித் திறனுக்காக உலகளாவிய கல்வித் தரத்தில் உருவாக்கப்பட்டுள்ளன. தேர்வுகளுக்குத் தயாராகும் போது உங்கள் அதிகாரப்பூர்வ பாடப்புத்தகத்துடன் சரிபார்க்கவும்.
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