The CAT exam quantitative aptitude section includes several questions from the topic of probability. Probability is nothing but a chance that some event might occur. More formally, it calculates a numerical value between 0 and 1 that represents the likelihood that an event might occur. Thus it is important to remember that

- if the probability for an
**Event**to occur is 1 than that event is always certain to occur - if the probability is 0 then that event will never occur

It is widely used in almost every field especially in the field of economics and finance. Before we delve deep into probability let us first familiarise ourselves with few of the basic terms of probability that will be useful for you to prepare for CAT exam.

**Event:** Any subset of a sample space is called an event.

**Exhaustive events:** In probability theory, a system of events is called exhaustive, if at least one of the event of the system occurs. Ex. If a coin is tossed then Head and Tails forms exhaustive set of events.

**Mutually Exclusive events:** A set of events is called mutually exclusive events if the occurrence of one of them means the other event cannot occur.

**Random Experiment:** An experiment whose outcome has to be among a set of events that are known but the exact outcome of the random experiment is unknown.

**Sample Space:** The set of all possible outcomes in Random Experiment is known as Sample space.

**Independent Events:** When the occurrence of one event has no bearing on the probability of the other event.

$latex \displaystyle \text{Probability of an Event} \\ \text{= }\frac{{\text{Favourable Outcome}}}{{\text{Total Number of Outcomes}}}$

**Combination of Events :**

**AND/OR Event**

1)Probability of event A and event B occurring = p(A) $latex \displaystyle \times $ p(B)

2)Probability of event A or event B occurring = p(A) $latex \displaystyle +$ p(B)

**Example 1 :** The probability of A doing a task is $latex \displaystyle \frac{1}{3}$ and that of B is $latex \displaystyle \frac{1}{5}$. What is the probability that either of them completes the task.

Sol – Here the probability is of either A OR B doing the task

$latex \displaystyle \text{= p(A)+p(B) = }\frac{1}{3}+\frac{1}{5}=\frac{8}{{15}}$

**Example 2 :** Probability of A hitting the target is ΒΌ and that of B hitting the target is 1/7 then probability that both hit the target if they get one shot each is ?

Sol – We want A AND B both to hit the target

$latex \displaystyle \text{= p(A)}\times \text{p(B) = }\frac{1}{4}\times \frac{1}{7}=\frac{1}{{28}}$

**Here are some more solved examples for you to better understand the concept : **

**Example 3:** I have two children. One is a boy born on Tuesday. What is the probability I have two boys?

**An example for independent Events :**

**Example 4 :** I tossed a coin 5 times and every time it gave heads. What is the probability of getting tails in the sixth toss?

**Some more solved examples :**

**Example 5 : **What is the probability of there being 53 Sundays in a non-leap year?

**Example 6 :** Two points are placed randomly along the circumference of a circle. What is the probability that the chord drawn between them is longer than the radius of the circle?

**Example 7 :** You have 30 green, 22 red and 14 pink socks scattered across the floor in dark. Minimum how many socks should you grab to make a matching pair (assume that a pair has two identical socks)?

I hope these examples help you understand the fundamentals of probability for your CAT exam preparation. To explore our full range of videos, mocks and sectional tests click here.