## Abhishek Khurana is teaching live on Unacademy Plus

Abhishek Khurana 6 times 99 percentiler in CAT MBA from NMIMS 2009-2011 8 years of teaching experience

Modern Maths PROBABILITY

DERNATION OF PROBABILAY In mathematics means the ikelihood of the of an event. Examples of events . Tossing a coin with the head up Drawing a red pen from a pack of different coloured pens Drawing a card from a deck of 52 cards etc. . An event that occurs for sure is called a Certain event and its probability is 1. An event that doesn't occur at all is called an impossible event and its probability is 0 This means that all other possibilities of an event occurrence le between 0 and 1. This is depicted as follows where A is an event and PIA) is the probability of the occurrence of the event.

DERNATION OF PROBABILITY . Every event will have a set of possible outcomes. It is called the 'sample space. Consider the example of tossing a coin . When a coin is tossed, the possible outcomes are Head and Tail So, the sample space is represented as [H, T. Similarly when two coins are tossed, the sample space is {(HH), (HT (TH).(T,T]. . Basic formulae of probability: P(A)- (No. of ways A can occur)/(Total no. of possible outcomes)

COMPOUND PROBABILITY Compound probability is when the problem statement asks for the likelihood of the occurrence of more than one outcome. Formula for compound probability P(A or B) PA) +P(B)-P[A and B) where A and B are any two events. P(A or B) is the probability of the occurrence of at least one of the events. P(A and B) is the probability of the occurrence of both A and B at the same time.

Mutually exclusive events Mutually exclusive events are those where the occurrence of one indicates the non- occurrence of the other OR When two events cannot occur at the same time, they are considered mutually Note: For a mutually exclusive event, P(A and B) = 0.

Mutually exclusive events Example 1: What is the probability of getting a 2or a 5 when a die is rolled? Solution: Taking the individual probabilities of each number, getting a 2 is 1/6 and so is getting a 5. Applying the formula of compound probability, Probability of getting a 2 or a 5, P[2 or 5) P(2) +P(5)- P(2 and 5) z 1/6+ 1/6-0

INDEPENDENT EVENTS When multiple events occur, if the outcome of one event doesn't affect the outcome of the other events, they are called independent events. Say, a die is rolled twice. The outcome of the first roll doesn't affect the second outcome. These two are independent events Example 2: A coin is tossed twice. What is the probability of getting two consecutive fails ?

INDEPENDENT EVENTS Example 2: A coin is tossed twice. What is the probability of getting two consecutive fails ? Solution: Probability of getting a tail in one toss 1/2 The coin is tossed twice. So 1/2 1/2- 1/4 is the answer.

DEPENDENT EVENTS When two events occur, if the outcome of one event affects the outcome of the other, they are called dependent events Example 3: A pack contains 4 blue, 2 red and 3 black pens. If 2 pens are drawn at random from the pack,not replaced and then another pen is drawn. What is the probability of drawing 2 blue pens and 1 black pen?

DEPENDENT EVENTS Example 4: What is the probability of drawing a king and a queen consecutively from a deck of 52 cards, without replacement