can anyone solve all the question and plz dhare with me.This all are probabilty sums and i am doing all this without tution at home so anyone who can help me plz share with me all the answers to the questions.
Answers
When MS and MBA applicants ask us – ‘What are my chances of getting into Harvard?‘ or ‘What’s my probability of getting scholarships from Oxford?‘ we get tongue-tied. There are so many variables at play, it’s difficult to give an accurate answer.
But when you get probability questions in your GRE and GMAT exam syllabus, you don’t have to get flummoxed. Understanding the basic rules and formulas of probability will help you score high in the entrance exams.
Meaning and definition of Probability
As the Oxford dictionary states it, Probability means ‘The extent to which something is probable; the likelihood of something happening or being the case’.
In mathematics too, probability indicates the same – the likelihood of the occurrence of an event.
Examples of events can be :
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.
Either an event will occur for sure, or not occur at all. Or there are possibilities to different degrees the event may occur.
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 lie between 0 and 1.
This is depicted as follows:
0 <= P(A) <= 1
where A is an event and P(A) is the probability of the occurrence of the event.
This also means that a probability value can never be negative.
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 {(H,H), (H,T), (T,H), (T,T)}.
The probability of head each time you toss the coin is 1/2. So is the probability of tail.
Basic formula of probability
As you might know from the list of GMAT maths formulas, the Probability of the occurrence of an event A is defined as: