Probability Problem

Study Probability:

It is helpful for determining the number of incidence of event in the possible outcomes. Probability lies between 0 and 1.

Types of probability:

Single event Probability
Multiple events Probability
Study Single event Probability:


Example: A coin tossed; probability for getting head is a single event

Study Multiple events Probability:

It is helpful for the determining the number of occurrence in multiple event trail.

Example:  A die is tossed twice; probability of getting odd numbers is a multiple event

Let us solve some sample problems in probability.


Study Probability Example Problem 1:


If a coin is tossed.  Find the probability of getting a head.

Solution for the problem:

In the experiment of tossing a coin once, the number of possible outcomes is two — Head (H) and Tail (T).

Let E be the event ‘getting a head’.

The number of outcomes favorable to E, (i.e., of getting a head) is 1

Therefore,

P (E) = P (head) = Number of outcomes favorable to E / Number of all possible outcomes = `(1)/(2)`

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Study Probability Example Problem 2:


A bag contains a Black ball, a Brown ball and a Purple ball, all the balls being of the same size. David takes out a ball from the bag without looking into it. What is the probability that she takes out the

Purple ball?
Black ball?
Brown ball?
Solution for the problem:

David takes out a ball from the bag without looking into it. So, it is equally likely that she takes out any one of them.

Let Y be the event ‘the ball taken out is Purple’, B be the event ‘the ball taken out is Brown’, and R be the event ‘the ball taken out is Black’.

Now, the number of possible outcomes = 3.

The number of outcomes favorable to the event Y = 1

P(Y) = `(1)/(3)` ,   P(R) = `(1)/(3)`     P (B) = `(1)/(3)`

Question on Probability in a Class Room

Topic : Probability

Question : In a class of 72 students, 44 are girls and,of these, 12 are going to college. Of the 28 boys in the class, 9 are going to college. If a student is selected at random from the class, what is the possibility that the person chosen is not going to college

Answer :
Not going to college means complement that students goes to college
So 1 is the probability that student goes to college
and no of students going to college is given by 9+12/72 = 7/24
= 1 - 7/24 = 24-7 / 24 = 17/24