1). What is the probability that a card drawn at random from a pack of 52 cards either a king or a spade?
View Answer Correct Answer: 4/13 Required probability = \( \large\frac{3}{52} + \frac{13}{52} = \frac{16}{52} = \frac{4}{13} \) [Hint 13 / 52 because there are 13 spades and 3 / 52 instead of 4 / 52 (there are four kings) because one king is already counted in spades.]
 
2). A card is drawn from a wellshuffled pack of cards. The probability of getting a queen of club or a king of heart is
View Answer Correct Answer: 1/26 Total ways = 52 There is one queen of club and one king of heart. Favourable ways = 1 + 1 = 2 Required probability = 2 / 52 = 1 / 26
 
3). One card is drawn at random from a wellshuffled pack of 52 cards. What is the probability that the card is either a red card or a king?
View Answer Correct Answer: 7/13 Total number of cards = 52 Total number of red cards = 26 Total number of kings = 4 But 2 red cards are also kings, So probability = \( \large\frac{26}{52} + \frac{4}{52}  \frac{2}{52} = \frac{26 + 4  2}{52} = \frac{28}{52} = \frac{7}{13} \)
 
4). A single letter is selected at random from the word "PROBABILITY". The probability that it is a vowel, is
View Answer Correct Answer: 4/11 Total number of letters = n(S) = 11 Whereas, number of vowels = n(E) = 4 Required probability = \( \large\frac{n(E)}{n(S)} = \frac{4}{11} \)
 
5). The probability that a leap year selected at random contains 53 Sundays, is
View Answer Correct Answer: 2/7 In a leap year there are 366 days. It means 52 full weeks + 2 odd days. These two day can be (Mon  Tues),(Tues  Wed),(Wed  Thu), (Thu  Fri), (Fri  Sat), (Sat  Sun) or (Sun Mon) So required probability =\( \large\frac{2}{7} \)
 
6). The probability of drawing a red card from a deck of playing cards is
View Answer Correct Answer: 1 / 2 Total number of cards n(S) = 52 Number of red cards n(E) = 26 P(E) = \( \large\frac{n(E)}{n(S)} = \frac{26}{52} = \frac{1}{2} \)
 
7). The probability of getting a composite number when a sixfaces unbiased die is tossed, is
View Answer Correct Answer: 1 / 3 n(S) = 6; n(E) = (4 , 6) = 2 p(E) = 2 / 6 = 1 / 3
 
8). If three unbiased coins are tossed simultaneously, then the probability of exactly two heads, is
View Answer Correct Answer: 3 / 8 n(S) = \( 2^3 \) = 8 Let E = Event of getting exactly two heads = {(H,H,T),(H,T,H),(T,H,H)} =n(E) = 3 Required probability = 3 / 8
 
9). Let E be the set of all integers with 1 at their unit places. The probability that a number chosen from {2,3,4,......50} is an element of E, is
View Answer Correct Answer: 4 / 49 n(S) = 49 Favourable numbers are 11, 21,31, 41 Required probability = 4 / 49
 
10). When two dice are rolled, what is the probability that the sum of the numbers appeared on them is 11?
View Answer Correct Answer: 1 / 18 n(S) = 36 n(E) = {(5,6),(6,5)} = 2 p(E) = \( \large\frac{n(E)}{n(S)} = \frac{2}{36} = \frac{1}{18} \)

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