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1). What is the probability that a card drawn at random from a pack of 52 cards either a king or a spade?
A). 17/52
B). 4/13
C). 3/13
D). 13/52
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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 well-shuffled pack of cards. The probability of getting a queen of club or a king of heart is
A). 1/52
B). 1/26
C). 1/13
D). 1/39
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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 well-shuffled pack of 52 cards. What is the probability that the card is either a red card or a king?
A). 1/3
B). 7/13
C). 10/13
D). None of these
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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
A). 3/11
B). 4/11
C). 2/11
D). 0
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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
A). 7/366
B). 26/183
C). 1/7
D). 2/7
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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
A). 2/18
B). 1/13
C). 1 /4
D). 1 / 2
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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 six-faces unbiased die is tossed, is
A). 1 / 4
B). 1 / 3
C). 1 / 2
D). 1
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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
A). 1 / 8
B). 2 / 8
C). 3 / 8
D). 4 / 8
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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
A). 5 / 49
B). 4 / 49
C). 3 / 49
D). 2 / 49
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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?
A). 1 / 6
B). 1 / 18
C). 1 / 9
D). 1
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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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