# Problem Solving Practice Test 4

#### Q.1

There are three events A, B and C one of which must happen. At a time only one can happen. The odds are 8 to 3 against A, 5 to 2 against B , find the odds against C.

- A. 3:8
- B. 43:34
- C. 34:43
- D. 34:77
- E. 43:77
- Answer: B

#### Q.2

One of two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.

- A. 2:5
- B. 3:5
- C. 5:3
- D. 2:3
- E. 3:2
- Answer: D

#### Q.3

In a class the probability of all the students passing the mathematics examination is 0.8 that of the whole class passing the Hindi examination is 0.7. If the probability of the whole class passing in at least one of the two exams is 0.95, then find the probability of not getting any failures in the whole class in both mathematics and Hindi.

- A. 0.15
- B. 0.55
- C. 1.75
- D. 1.05
- E. 0.25
- Answer: B

#### Q.4

In an entrance test that is graded on the basis of English and general knowledge, the probability of a randomly chosen student passing both the tests is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English test is 0.75, then what is the probability of passing the general knowledge test?

- A. 1/20
- B. 3/5
- C. 13/20
- D. 5/13
- E. 11/20
- Answer: C

#### Q.5

In a lottery of 50 tickets numbered 1 to 50, two tickets are drawn simultaneously. Find the odds in favour that none of the tickets has a prime number.

- A. 12:17
- B. 1:10
- C. 5:11
- D. 17:12
- E. 17:18
- Answer: E

#### Q.6

There are 9 letters; 5 consonants and 4 vowels. Three letters are chosen at random. What is the probability of choosing more than one vowel?

- A. 3/5
- B. 4/15
- C. 17/42
- D. 15/42
- E. 1/21
- Answer: C

#### Q.7

A bag contains 50 tickets numbered 51,52,???,100 of which 5 are drawn and arranged in ascending order of magnitude.find the probability that the third number is 80.

- A. 551/312500
- B. 551/15134
- C. 340/15134
- D. 3364/312500
- E. 30856/3125000
- Answer: B

#### Q.8

Four persons are to be chosen from a group of 3 men, 2 women and 4 children. Find the probability of choosing exactly 2 women.

- A. 3/50
- B. 12/25
- C. 1/5
- D. 1/6
- E. 1/7
- Answer: D

#### Q.9

A bag contains tickets numbered 1 to 30. Three tickets are chosen at random. Find the probability that all the tickets have two digit numbers.

- A. 11/58
- B. 19/58
- C. 21/30
- D. 2/3
- E. 5/8
- Answer: B

#### Q.10

The letters of the word SOCIETY are arranged at random in a row. What is the probability that the three vowels come together?

- A. 12/49
- B. 1/42
- C. 3/7
- D. 1/7
- E. 1/5
- Answer: D

#### Q.11

What are the odds in favour that when the letters of the word UNIVERSITY are arranged randomly, the I???s come together?

- A. 2:3
- B. 1:4
- C. 3:4
- D. 2:5
- E. 1:3
- Answer: B

#### Q.12

Out of 10 toppers of a school, 5 are girls and 5 are boys. 5 students have to be chosen to represent the school in a seminar. Find the probability that all five are girls.

- A. 3/50
- B. 1/28
- C. 1/10
- D. 1/5
- E. 1/252
- Answer: E

#### Q.13

In a lottery a person chooses 6 different numbers from 1 to 20. If these numbers match with the six numbers chosen by the lottery committee then he wins the lottery. What is his probability of winning the prize?

- A. 1/1615
- B. 1/6460
- C. 1/19380
- D. 1/387
- E. 1/38760
- Answer: E

#### Q.14

100 students appeared in two examinations. 60 passed the first, 50 passed the other and 30 passed both. Find the probability that a student selected at random has failed in exactly one.

- A. 1/6
- B. 1/2
- C. 1/3
- D. 1/4
- E. 1/5
- Answer: B

#### Q.15

A card is drawn from a pack of cards. Find the probability that it is an ace or a diamond or a red card.

- A. 1/52
- B. 1/2
- C. 11/13
- D. 5/13
- E. 7/13
- Answer: E