# Probability

# Introduction:

**Probability is merely a subtype of Permutation and Combination (PnC) concept.**

**Probability can be solved without mugging up formulae if your basic concepts are clear.**

**Probability is based on observations of certain events. The probability of an event is the ratio of the number of observations of the event to the total numbers of the observations.**

**This chapter is considered a tricky one by many CAT aspirants ****and hence, a clear understanding of the concept is required. It is very ****an important topic for CAT and other MBA entrance exams, usually, ****2–3 questions are asked in CAT exam either directly or indirectly**

**as an application in probability.**

# Fundamental principle of counting:

Multiplication rule : Use this rule whenever the conjuction ‘and’ matters.

Addition Rule: Use this rule whenever the conjunction ‘or’ matters

For example:

**A college offers 6 courses in the morning and 4 in the evening. Find the possible number of choices with the ****student if he wants to study one course in the morning and one in the evening.**

**The college has 6 courses in the morning out of which**

** the student can select one course in 6 ways**

**In the evening the college has 4 courses out of which the student**

** can select one in 4 ways.**

** Hence the required number of ways = 6 × 4 = 24.**

### This is the example for Multiplication rule.

**A college offers 6 courses in the morning and 4 ****in the evening. Find the number of ways a student can select ****exactly one course, either in the morning or in the evening**.

**The college has 6 courses in the morning out of which**

** the student can select one course in 6 ways.**

** In the evening the college has 4 courses out of which the student**

** can select one in 4 ways.**

** Hence the required number of ways = 6 + 4 = 10.**