**Types of Probability CAT Questions**

To solve Probability CAT Questions, one must have a clear understanding of the concepts of Permutation and Combination. To master this area, one must brush up on their knowledge of permutation and combination. Probability CAT Questions are logical in nature and one should be aware of the types of questions to solve them easily. Below mentioned are some of the types of Probability CAT Questions:

- Bayes Theorem
- Dependent Events/ Independent Events/ Mutually Exclusive Events
- Conditional Probability
- Multiplication Rule of Probability

**Formulas for Probability CAT Questions**

**Probability**: The probability formula is used to compute the probability of an event. In other words, the likelihood of happening an event is called probability.

**Random Experiments:**An experiment is called a random experiment, if it satisfies the following two conditions: (i) It has more than one possible outcome. (ii) It is not possible to predict the outcome in advance.**Outcomes:**A possible result of a random experiment is called an outcome.**Sample Space:**The set of all possible outcomes is called Sample Space.- Probability of an event A [P(A)] = 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 favorable? 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬 𝐓𝐨𝐭𝐚𝐥 𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬 Or, P(A) = 𝐧(𝐀) 𝐧(𝐒) Where ➢ P(A) is the probability of an event “A”. ➢ n(A) is the number of favorable outcomes of event A. ➢ n(S) is the sample space Ex: What is the probability of getting a jack from a well-shuffled pack of cards? Sol: Here, n(S) = 52 and n(E) = 4 (Total 4 jacks) Hence, required probability = P (E) = n(E) n(S) = 4 52 = 1 13 .
- Range of probability of an event A: 0 ≤ P(A) ≤ 1
**Odds: a. Odds in favor =**𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 favorable? 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 unfavorable? 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬 b. Odds against = 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 unfavorable? 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬 𝐍𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 favorable? 𝐨𝐮𝐭𝐜𝐨𝐦𝐞?**Addition Rule:**P(A U B) = P(A) + P(B) – P(A∩B)**Multiplication Rule:**P(A ∩ B) = P(A) P( B A ) = P(B) P( A B )**Equally likely events:**When two or more events have an equal chance of happening or equal probability of occurrence, then those events are called equally likely events.**Independent events:**When two events have occurred, then the probability of occurrence of one event is not affected by the occurrence and non-occurrence of the other event, then the two invents will be called the independent event. For Independent events A and B: P( B A ) = P(B) and P( B A ) = P(B) So, P(A ∩ B) = P(A) . P(B)**Complementary events:**When two events have occurred, such that if one of the events happens, then the other event cannot happen and vice versa. Complimentary event of event A is denoted by A' or A̅. For complimentary events A and A' or A̅: P(A) + P(A’) = 1**Exhaustive events:**When two or more events have occurred. then all such that if one of the events happens, then the other event cannot happen and vice versa. For Exhaustive events A, B, C, … : P(A) + P(B) +P(C)… = 1**Mutually exclusive events:**Two events are mutually exclusive if they cannot occur at the same time. In another word, mutually exclusive events are disjoint events. So, the intersection of two disjoint events is an empty event. If two events are disjoint, then the probability of them both occurring at the same time is 0. If events E1 and E2 are mutually exclusive events, then- a. E1 E2 = b. P(E1 E2) = 0 c. P (E1 U E2) = P(E1) + P(E2)
**Conditional Probability:**P(A | B) = P(A ∩ B) P(B)

**Example 1: **A box contains 3 red balls, 3 blue balls, and 7 green balls. If two balls are drawn at random then what is the probability that both the balls are nongreen?

**Example 2:** Calculate the probability of getting an even number, if a dice is rolled.

**Sample Probability CAT Questions**

Listed below are some of the sample Probability CAT Questions. The candidates can go through the below-mentioned CAT Questions to ace the quantitative ability section of the CAT Exam. The Probability CAT Questions given below will provide the candidates with an overview of the type of questions that are asked on this topic.

You must also go through Probability CAT Questions from the previous year to gain a better understanding of the kind of questions asked. Download CAT Question Paper to practice.

**Question 1: **In the MBA Programme of a B - School, there are two sections A and B. 1/4th of the students in Section A and 4/9th of the students in section B are girls. If two students are chosen at random, one each from section A and Section B as a class representative, the probability that exactly one of the students chosen is a girl, is:

**Answer:** 17/36

**Explanation:** Selecting a girl from section A and section B is 1/4 and 4/9 respectively.

Selecting a boy from section A and section B is 3/4 and 5/9 respectively.

Case 1: A girl from section A and a boy from section B.

Case 2: A boy from section A and a girl from section B.

**Question 2:** If 2 dice are thrown simultaneously, what is the probability that 1 of them shows up ‘2’ and the other shows ‘5’?**Answer:** 1/18

**Explanation:** Total number of outcomes = 6 x 6 = 36

There are 2 favorable circumstances = (2,5) and (5,2)

Hence, 2/36 = 1/18

**Question 3:** A box contains 5 green, 3 black, and 7 red balls. Two balls are selected at random without replacement from the box. What is the probability that both balls are red?

**Answer:** 1/5

**Explanation: **Total number of balls = 5 + 3 + 7 = 15.

The number of ways in which 2 balls can be selected = 15C2 = (15×14)/(2×1) = 105

Total number of red balls = 7

The number of ways in which 2 red balls can be taken out = 7C2 = (7×6)/(2×1) = 21

The probability of getting 2 red balls = 21/105 = 1/5.

Alternative solution:

The probability of the first ball being red = 7/15.

If the first ball taken out is red, the box, now, has a total of 14 balls of which 6 are red.

The probability of the 2nd ball being red = 6/14

The probability of both balls being red is (7/15)×(6/14) = 1/5.

**Note:** Here we have to get a red ball in each of the draws and hence we do not have to consider any arrangement, but if we draw balls of different colours, the arrangement will have to be taken into account.

**Question 4:** If P(A|B) = 1/3, P(B) = 1/4, and P(A) = 1/2, the probability that exactly one of these events A and B occur is:

**Answer: **7/12

**Explanation:**

Or,

So, we have P(A) = 1/2 and

Therefore, P (only A) = P(A) – P(A ⋂ B)

= 1/2 – 1/12 = 5/12.

Similarly, P(B) = 1/4 and P(A ⋂ B) = 1/12

Therefore, P(only B) = P(B) – P(A ⋂ B)

= 1/4 – 1/12 = 1/6.

Probability that exactly one of A and B happens = P(only A) + P (only B)

= 5/12 + 1/6 = 7/12.

**Question 5:** What is the probability of rolling three six-sided dice, and getting a different number on each die?

**Answer: **5/9

**Explanation:** For the first die, we can roll any one of six numbers.

For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities.

For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.

6 x 5 x 4 = 120 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6 = 216).

120/216 = 5/9

**Probability CAT Questions PDF**

It is advised to the candidates to practice Probability CAT Questions in order to solve questions on Modern Mathematics. Solving past year's papers and CAT mock tests will help the candidates to understand the different types of questions that can be asked on this topic. Candidates can download the Probability CAT Questions PDF given below:

**Probability CAT Questions - Download PDF**

**Best Books to Solve Probability CAT Questions**

In order to ace the Quantitative Ability section of the CAT exam, the candidates need to refer to the best books and study material. Candidates can also refer to the NCERT books of classes 9 and 10 to practice Probability CAT Questions. The candidates must refer to the books which contain all the types of questions related to Probability CAT Questions.

**Tips to Solve Probability CAT Questions**

The candidates aspiring to take the CAT exam need to know the tips and tricks to solve Probability CAT Questions. Candidates should go through the below-mentioned points in order to know the tips to solve Probability CAT Questions.

- Candidates should first start practicing questions based on Permutation and Combination in order to solve Probability CAT Questions quickly and easily.
- CAT exam consists of negative marking so it is very important to choose the correct set of questions. As not many questions are asked from Probability the candidates should only select those questions that they are sure about.
- The candidates should practice previous year's papers and mock tests to know the types of questions that can be asked on this topic.

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