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01. One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card (Jack, Queen and King only)?
A. 1/13 B. 3/13
C. 1/4 D. 9/52

Answer and Explanation

Answer: 3/13

Explanation:
Clearly, there are 52 cards, out of which there are 12 face cards.
P (getting a face card) = 12/52 = 3/13 .

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02. A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is: 
A. 1/22 B. 3/22
C. 2/91 D. 2/77

Answer and Explanation

Answer: 2/91

Explanation:

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03. In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize? 
A. 1/10 B. 2/5
C. 2/7 D. 5/7

Answer and Explanation

Answer: 2/7

Explanation:
P (getting a prize) = 10/(10 + 25) = 10/35 = 2/7 
    

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04. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green? 
A. 1/3 B. 3/4
C. 7/19 D. 8/21
E. 9/21

Answer and Explanation

Answer: 1/3

Explanation:

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05. Two friends A and B apply for a job in the same company. The chances of A getting selected is 2/5 and that of B is 4/7. What is the probability that both of them get selected?
A. 8/35  B. 34/35
C. 27/35 D. None of these

Answer and Explanation

Answer: 8/35 

Explanation:
P(A) = 2/5
P(B) = 4/7
E = {A and B both get selected}
P(E) = P(A)*P(B)
= 2/5 * 4/7
= 8/35

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06. Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?
A. 9/25 B. 9/50
C. 18/25 D. None of these

Answer and Explanation

Answer: 9/25

Explanation:
S = {1, 2, 3, … , 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18
P(E) = n(E)/n(S) = 18/50
= 9/25

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07. In a basket that contains 10 fruits, 4 are rotten, if three fruits are drawn from the basket, find the probability that none of the fruits drawn is rotten?
A. 6/10 B. 6C3 / 10C3
C. 6 / 10C3 D. 3 / 10C3

Answer and Explanation

Answer: 6C3 / 10C3

Explanation:
The basket contains 6 good and 9 rotten fruits.
=> P(drawing 3 good fruits) = 6C310C3

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08. The probability that a given problem will be solved by A, B and C are 2/3, 5/7 and 4/5 respectively. Find the probability of the problem being solved?
A. 40/105 B. 101/105
C. 103/105 D. None of the above

Answer and Explanation

Answer: 103/105

Explanation:
 Given P(A) = 2/3, P(B) = 5/7 and P(C) = 4/5
=> Probability of problem being solved
=> P(A U B U C) = 1 – (A ᴖ B ᴖ C)
=> 1 – P(A), P(B) P(C)
=> = 1 P(A dash) P(B dash) P(C dash)
=> = 1 – 1/3(2/7)(1/5) = 1 – 2/105
P(A U B U C) = 103/105

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09. If a card is drawn from a well shuffled pack of cards, then find the probability that the card drawn is a numbered card
A. 6/13 B. 29/52
C. 40/52 D. 9/13

Answer and Explanation

Answer: 9/13

Explanation:
A card can be drawn from a pack of cards in 52C1 ways i.e, n(S) = 52
=> There are 36 numbered cards, of which one card can be drawn in
=> 36C1 ways, i.e., n(E) = 36.

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10. A coin is tossed 10 times. Find the probability of obtaining head at least once.
A. 1/210 B. 10/210
C. 9/210 D. 210 – 1 / 210

Answer and Explanation

Answer: 210 – 1 / 210

Explanation:
Let E be the event of heads occurring at least once and E- be the event of heads not occurring at all i.e. all tails.
=> P(E) = 1 – P(E dash)
=> 1 – ½10 = 210 – 1 / 210

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