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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.

1/2

B.

3/4

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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Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is :

A.

2/9

B.

1/9

C.

8/9

D.

7/9

Answer with explanation

Answer: Option BExplanation

One person can select one house out of 3= 3C13C1 ways =3.

Hence, three persons can select one house out of 3 in 3 x 3 x 3 =9.

Therefore, probability that all thre apply for the same house is 1/9

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Two brother X and Y appeared for an exam. The probability of selection of X is 1/7 and that of B is 2/9. Find the probability that both of them are selected.

A.

1/63

B.

1/14

C.

2/63

D.

1/9

Answer with explanation

Answer: Option CExplanation

Let A be the event that X is selected and B is the event that Y is selected.

P(A) = 1/7, P(B) = 2/9.

Let C be the event that both are selected.

P(C) = P(A) × P(B) as A and B are independent events:

= (1/7) × (2/9) = 2/63

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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.

3/5

C.

8/21

D.

7/21

Answer with explanation

Answer: Option AExplanation

Total number of balls = (8 + 7 + 6) = 21.

Let E = event that the ball drawn is neither red nor green

= event that the ball drawn is blue.

n(E) = 7.

P(E) = n(E)/n(S) = 7/21 = 1/3.

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A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.

A.

23/42

B.

19/42

C.

7/32

D.

16/39

Answer with explanation

Answer: Option BExplanation

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A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?

A.

136/345

B.

17/87

C.

316/435

D.

158/435

Answer with explanation

Answer: Option CExplanation

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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.

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 race where 12 cars are running, the chance that car XX will win is 1/6, that YY will win is 1/10 and that ZZ 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.

1/240

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.

343/1728

B.

21/36

C.

12/35

D.

7/44

Answer with explanation

Answer: Option DExplanation

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A box contains 100 balls, numbered from 1 to 100. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?

A.

1/2

B.

3/4

C.

3/8

D.

1/8

Answer with explanation

Answer: Option AExplanation

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