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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 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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From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first is a red card and the second is a king is -.

A.

3/52

B.

1/26

C.

11/26

D.

15/26

Answer with explanation

Answer: Option BExplanation

Let E_{1} be the event of drawing a red card.

Let E_{2} be the event of drawing a king .

P(E_{1} ∩ E_{2}) = P(E_{1}) . P(E_{2})

(As E_{1} and E_{2} are independent)

= 1/2 * 1/13 = 1/26

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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.

1/5

C.

9/10

D.

6/5

Answer with explanation

Answer: Option BExplanation

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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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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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.

4/7

B.

3/8

C.

5/9

D.

1/6

Answer with explanation

Answer: Option AExplanation

Explanation: 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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In a race where 12 cars are running, the chance that car X will win is 1/6, that will win is 1/10 and that Z will win is 1/8. Assuming that a dead heat is impossible. Find the chance that one of them will win.

A.

47/120

B.

1/480

C.

1/160

D.

1/180

Answer with explanation

Answer: Option AExplanation

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A bag contains 7 green and 5 black balls. Three balls are drawn one after the other. The probability of all three balls being green, if the balls drawn are not replaced will be:

A.

7/44

B.

12/35

C.

21/36

D.

343/1728

Answer with explanation

Answer: Option AExplanation

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A.

3/7

B.

4/7

C.

1/8

D.

3/4

Answer with explanation

Answer: Option BExplanation

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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In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ?

A.

6/7

B.

19/21

C.

7/31

D.

5/21

Answer with explanation

Answer: Option CExplanation

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁)

As remaining person can be any one among three couples left.

Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅

= (10 x 6)/252 = 5/21

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There are 10 Letters and 10 correspondingly 10 different Address. If the letter are put into envelope randomly, then find the Probability that Exactly 9 letters will at the Correct Address ?

A.

1/10

B.

1/9

C.

1

D.

0

Answer with explanation

Answer: Option DExplanation

As we know we have 10 letter and 10 different address and one more information given that exactly 9 letter will at the correct address….so the remaining one letter automatically reach to their correct address

P(E) = favorable outcomes /total outcomes

Here favorable outcomes are ‘0’.

So probability is ‘0’.

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