Probability in Math

Introduction to Probability

In math,Probability is used to get the feasible outcomes in an event. It is definite as the ratio between the numbers of positive outcomes to the total number of outcomes. The importance of probability lies only between 0 and 1. The Conditional probability and  the Theoretical probability is the types of  the probability in math.


Example1:


In math the examples of probabilities is as follows.

1)In a vehicles parking area 200 vehicles are parked. There are 50 are cars, 40 are vans and the remaining are lorries. If all vehicles are similarly possible to leave, find the probability in math of.

a) First leaving the lorry.

b) First leaving the van.

c) First leaving the car.

Solution:

a) Let s be the sample space and A be the event of a lorry leaving first.

n(S) =200

n(A)= 200-50-40= 110

probability of a lorry leaving first:

P(A)= 110/200

=11/20

b) Let B be the event of a van leaving first

n(S)=200

n(B) =40

Probability of a van leaving first:

P(B)=40/200

= 4/50

c) Let c be the event of a car leaving first

n(S)=200

n(C)=50

Probability of a car leaving first:

P(C)=50/200

=5/40.

I have recently faced lot of problem while learning Volume of Pyramid, But thank to online resources of math which helped me to learn myself easily on net.

Example2:


In math, the another example of probability is as follows,

2)An analysis was taken on 20 groups at a college to find the total number of left-handed students in each class.

Quick Probability Math

Quick Probability math Introduction:

Quick Probability is study of math. Probability is number of outcomes is divided into total number of events. The probability is also the expected value of the math. These are the two kinds of distribution are used discrete and continuous distribution.  The general format of the formula for quick probability

The probability of Event P (A) =` ("Number of outcomes na(a)")/("Total Number of events n(s)")`

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Quick Probability math Examples:


Quick Probability math– Example 1:

Toss three coins and find the probability of two tails. The possible outcomes are:

Solution:

Step 1:

n (s) = {TTT, TTH, THT, THH, HTT, HTH, HHT, HHH}=8

Step 2:

There are 3 tosses with only two tails:

n (a) = {TTH, THT, HTT}=3

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) =` 3/8.`

Quick Probability math– Example 2:

To toss three coins and get the probability of two head and so one tails. The possible outcomes are:

Solution:

Step 1:

n (s) = {TTTT, TTTH, TTHT, TTHH, HTTT, HTTH,THHT, HTHH, THTT, TTHH, THHT, HTHH, HTHT, HTHH,HHHT, HHHH }=16

Step 2:

There are 3 tosses with only one head:

n (a) = { TTHH, HHTT, HTTH, THHT, HTHT, THTH}=6

Step 3:

Formula:

P (A) = n(a)/n(s)

Answer:

P (A) = `6/16.`

Quick Probability math Example 3:

Roll a dice; find the probability of obtain number 5.

Solution:

Total Number of possible = n (a) = {1, 2, 3, 4, 5, 6}

n (s) = 6

The number of outcomes n (a) = {5}

n (a) = 1

The probability of getting value = `1/6` .

Quick Probability math Example 4:

A coin is tossed. If the coin land on top of a container is filled with one black globe and three white spheres. If the coin landed on tails the container is filled with one black sphere and nine white spheres. A sphere is then selected from the container. What is the probability that the sphere selected is black?

Solution

Let H = Heads, T = Tails and B = Black sphere selected. Then by the law of total probability

P(B) = P(B|H)P(H) + P(B|T)P(T)

= (0.25)(0.5) + (0.1)(0.5)

P (B) = 0.175

Is this topic Conditional Probability Definition hard for you? Watch out for my coming posts.

Quick Probability math practice problems:


Quick Probability math Practice problem 1:

To tossing the coin in one time what is the probability of get Head?

Quick Probability math Practice Problem 2;

If through the dice in one time what is the probability of get 6?

Quick Probability math Practice Problem 3:

If the probability of being correct is .95

Answer key:

½

`1/6`

0.05