**Introduction:**

### Probability is a super-fascinating topic that keeps on your toes. Along with mathematical ability, it requires a combination of quick thinking and reasoning skills in order to crack these exams quickly. An important part of CAT quantitative aptitude section, it is important you practice problems for this topic. We bring this five-problem set with the same intent and purpose.

**Question 1: **Let A and B be two events such that

Where Ā stands for complement of event A. Then, events A and B are

(a) Mutually exclusive

(b) Independent but not equally likely

(c) Equally likely but not independent

(d) Equally likely and mutually exclusive

### Answers and Explanations

**Question 2:** 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) 7/9

(b) 8/9

(c) 1/9

(d) 2/9

### Answers and Explanations

**Option c**

All the three persons has three options to apply a house.

Therefore total number of cases = 3^{3}

Now, favorable cases = 3 (All can apply for house 1 or 2 or 3)

Therefore required probability = {3/(3^{3})} = 1/9

**Question 3:** The probability that A speaks truth is 4/5 while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact, is

(a) 7/20

(b) 1/5

(c) 3/20

(d) 4/5

**Question 4:** Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse, is

(a) 4/5

(b) 3/5

(c) 1/5

(d) 2/5

### Answers and Explanations

**Option (d)**

The probability that Mr. A selected the loosing horse = 4/5 x ¾ = 3/5

The probability that Mr. A selected the winning horse = {1 – (3/5)} = 2/5

**Question 5:** Events A, B, C are mutually exclusive events such that

The set of possible values of x are in the interval

(a) 1/3 , ½

(b) 1/3, 2/3

(c) 1/3, 13/3

(d) 0,1