Probability is one of the most important chapters in the syllabus of WBJEE Entrance Examination. About **2-4 questions** are being asked from this chapter in WBJEE examination.

In this article you will get chapter notes of **Probability** for WBJEE Entrance Examination 2018. These notes will help all WBJEE aspirants to understand the concept of Probability in an easiest possible way.

**About the Chapter Notes:**

After the detailed analysis of previous year papers of WBJEE Examination, the Subject Experts of Mathematics have prepared these chapter notes of Probability including all important topics like Condition probability, independent events, theorem of total probability, Bayes’ theorem, Bernoulli trails etc.

**About the exam:**

West Bengal Joint Entrance Examination (WBJEE) is a state level common entrance test organized by West Bengal Joint Entrance Examinations Board for admission to the Undergraduate Level Engineering and Medical Courses through a common entrance test in the State of West Bengal.

**Important Questions and Preparation Tips - Matrices and Determinants**

**Important Concepts:**

**Important Questions and Preparation Tips - Complex Numbers**

**Some previous years solved questions are given below:**

**Question 1:**

Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is

(A) 24800

(B) 25100

(C) 25200

(D) 25400

**Solution 1:**

^{7}C_{3} X ^{4}C_{2 }X 5! = 25200

Hence, the correct option is (C).

**Important Questions and Preparation Tips – Relations and Functions**

**Question 2:**

Ram is visiting a friend. Ram knows that his friend has 2 children and 1 of them is a boy. Assuming that a child is equally likely to be a boy or a girl, then the probability that the other child is a girl, is

(A) 1/2

(B) 1/3

(C) 2/3

(D) 7/10

**Solution 2:**

Let us denote the boy with *B* and the girl with *G*. Let S be the sample space for two children and one of them is boy.

S = {BG, BB,}

The probability that one of the children is boy and the other is girl = 1/2

Hence, the correct option is (A).

**Important Questions and Preparation Tips – Sequence and Series**

**Question 3:**

If 5 distinct balls are placed at random into 5 cells, then the probability that exactly one cell remains empty is

(A) 48/125

(B) 12/125

(C) 8/125

(D) 1/125

**Solution 3:**

If we have to keep exactly one cell empty, then one of the cell must contain 2 balls and the remaining cell must contain one ball each.

Now let us assume two balls as one unit.

So, we have now 4 units to be arranged in 4 places.

This can be done in 4! ways.

Hence, the correct option is (A).

**Important Questions and Preparation Tips – Permutation and Combination**

**Question 4:**

A survey of people in a given region showed that 20% were smokers. The probability of death due to lung cancer, given that a person smoked, was 10 times the probability of death due to lung cancer, given that a person did not smoke. If the probability of death due to lung cancer in the region is 0.006, what is the probability of death due to lung cancer given that a person is a smoker?

(A) 1/140

(B) 1/70

(C) 3/140

(D) 1/10

**Solution 4:**

Let us assume that,

S = person is smoker

NS = person is non smoker

D = death due to lung cancer

Hence, the correct option is (C).

**Important Questions and Preparation Tips – Binomial Theorem**

**Question 5:**

A person goes to office by a car or scooter or bus or train, probability of which are 1/7, 3/7, 2/7 and 1/7 respectively. Probability that he reaches office late, if he takes car, scooter, bus or train is 2/9, 1/9, 4/9, and 1/9 respectively.

Given that he reached office in time, the probability that he travelled by a car is

(A) 1/7

(B) 2/7

(C) 3/7

(D) 4/7

**Solution 5:**

Hence, the correct option is (A).

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