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A Learning Portal from Recruitment India

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 with explanation

Answer: Option BExplanation

Clearly, there are 52 cards, out of which there are 12 face cards.

Probability of getting a face card = 12/52 = 3/13

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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 with explanation

Answer: Option AExplanation

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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The probability that Soumya will get marry within 365 days is ‘a’ and the probability that her colleague Alma get marry within 365 days is ‘b’. Find the probability that only one of the two gets marry at the end of 365 days.

A.

a-b-2ab

B.

a+b-2ab

C.

a-b+2ab

D.

ab-a-b

Answer with explanation

Answer: Option BExplanation

The probability that Soumya will get marry than Alma will be =a(1-b).

Similarly, The probability that Alma will get marry than Soumya will be b(1-a).

The probability thateither of these two get marry =a(1-b) +b(1-a) =a+b-2ab.

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10 books are placed at random in a shelf. The probability that a pair of books will always be together is -.

A.

1/10

B.

9/10

C.

1/5

D.

1/10

Answer with explanation

Answer: Option CExplanation

10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!

Required probability = 1/5

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There are 8 boys and 12 girls in a class. 5 students have to be chosen for an educational trip. Find the number of ways in which this can be done if 2 particular girls are always included.

A.

805

B.

816

C.

961

D.

1050

Answer with explanation

Answer: Option BExplanation

18c3 = 816 (2 girls already selected).

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A bag contains 6 black and 8 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?

A.

1/8

B.

5/9

C.

4/7

D.

3/8

Answer with explanation

Answer: Option CExplanation

Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

P (drawing a white ball) =8/14=4/7

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A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good.

A.

6/63

B.

2/63

C.

125/126

D.

1/126

Answer with explanation

Answer: Option CExplanation

Required probability = 1 – 1/126 = 125/126

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Determine the probability that a digit chosen at random from the digits 1, 2, 3, …12 will be odd.

A.

1/2

B.

4/9

C.

1/9

D.

5/9

Answer with explanation

Answer: Option AExplanation

Total no. of Digits = 12. Equally likely cases = 12.

There are six odd digits. Probability = 6 / 12 = 1 / 2

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There are 7 red balls and 8 yellow balls in a bag. Two balls are simultaneously drawn at random. What is the probability that both the balls are of same colour ?

A.

B.

C.

D.

Answer with explanation

Answer: Option DExplanation

Total balls in the bag = 7 + 8 = 15

Total possible outcomes = Selection of 2 balls out of 15 balls

= 15C_{2} = (15*14) / (1*2) = 105

Total favourable outcomes = Selection of 2 balls out of 8 yellow balls + Selection of 2 balls out of 7 red balls

= 8C_{2} + 7C_{2} = [(8*7)/(1*2)] + [(7*6)/(1*2)]

= 28 + 21 = 49

Required probability = 49/105 = 7/15

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There are four hotels in a town. If 3 men check into the hotels in a day then what is the probability that each checks into a different hotel?

A.

3/4

B.

1/4

C.

4/7

D.

3/8

Answer with explanation

Answer: Option DExplanation

Total no.on ways to stay in a hotel without any condition = 4 x 4 x 4 = 64 ways.

Bcoz, every person have 4 choices

Now, if every person has to stay in the different hotels then no.of ways = 4×3×2 = 24 ways.

Required probability =24/64 = 3/8

(or)

Total cases of checking in the hotels = 4 x 4 x 4 = 64 ways.

Cases when 3 men are checking in different hotels = 4×3×2 = 24 ways.

Required probability =24/64 = 3/8

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