Probability Survey

Author: nitin.p070

The probability survey is the way of expressing an event that will occur. The probability survey is the event, the experiments that are repeatedly done under some predefined conditions. The results for one or more experiments are not equal. These types of experiments are called as the random experiments or simply experiments. The probability includes the sample space, trail and different forms of events.

Terms present in the probability survey:

Sample space indicates the total number of possibilities for an experiment.
Trial corresponds to the experiment is performed.
Event specifies the outcome of the experiments.
Exhaustive events are an event which contains all the necessary possible outcomes of the experiment.
Mutually exclusive events are the two events that cannot occur simultaneously.
The probability certain likely defines the equally likely event in the probability. Equally likely event means that the two or more events have an equal probability. For example while tossing the die the probability for getting the tail and also the probability for getting the head are the equally likely events. The equally likely event determines the equal probability for the events.

Example problems for probability survey:

Ex 1 :A jar has 6 gray and 9 red marbles. What is the probability to get one gray marbles from the urn without replacement?

Sol:

The number of marbles in the jar is 6 gray and 9 red marbles.

The total numbers of marbles are 15 marbles.

The possibility for getting a gray ball is 6.

The required probability is 6/15 .

Ex 2 : While tossing a fair die, find the complementary probability of the numbers greater than 3.

Sol:

The sample space for the die is S= {1, 2, 3, 4, 5, 6}

The total number of sample space =6.

A is the event for getting the number greater than 3.

A= {4, 5, 6}

The number of events greater than 3 is n (A) =3

P (A) =n (A)/ n(S)

P (A) = 3/6

P (A) = 1/2

The probability for getting the numbers greater than 3 is 1/2 .

The formula for the complementary probability is 1- P (original probability).

The required probability = 1-P (A)

The required probability = 1- 1/2

The required probability = 1/2

The complementary probability for the numbers greater than 3 is 1/2 .

Survey of probability of certain likely events:

Some examples for probability certain likely:

Probability for getting the head and the tail when a coin is tossed only one time.
The probability for getting the number 3 and number 4 are equally likely events.
If an urn contains 5 white balls and 5 red balls. In that the probability for getting the single white ball and also the probability for getting the single red ball are the equally likely events.

Ex 3 : A jar has 5 gray and 7 green marbles. What is the probability to get one gray marbles and also probability for getting 1 green marbles? Determine whether the above events are equally likely events.

Sol:

The number of marbles in the jar is 5 gray and 7 green marbles.

The total numbers of marbles are 12 marbles.

The possibility for getting a gray marble is 5.

The probability for getting one gray marble is 5/12.

The possibility for getting a green marble is 7.

The probability for getting one green marble is 7/12.

The probabilities are 5/12 and also 7/12. These two probabilities are not the equally likely event because the probability of that two events are not same they are different.

Ex 4 : A single six face die is rolled. Find the probability for getting the number 6 and also 3. Determine whether these two events are equally likely events are not.

Sol:

The sample space for the die is S= {1, 2, 3, 4, 5, 6}

The total number of sample space is 6.

The probability for getting the number 3 is 1/6 .

The probability for getting the number 6 is 1/6 .

The probabilities for the two events are 1/6 and 1/6 respectively. The probabilities for the two events are equal. So these two events are equally likely events.

Practice problems:

Two coins are tossed at the same time. What is the probability to get two tails?
Ans: 1/2 .

Article Source: http://www.articlesbase.com/k-12-education-articles/probability-survey-6618083.html

About the Author

Understand more on about the Divide Fraction, and its Illustrations. Between, if you have issue on these Add Fraction keep verifying my content i will try to help you. Please discuss your feedback.