Tanchu Manchu

Hey Guys! Today we will discuss the term probability. What is probability? Probability is the likelihood of something occurring.Probability is like forecasting the likelihood of something happening. It helps us determine how likely an event is to occur. We define probability as a number between 0 (impossible) and 1 (certain). For example, a 10% chance of rain is considered a likelihood. Probabilities can be described using words such as unlikely, feasible, likely, or certain. 🎲🌦️ In mathematics, the probability of an event occurring is computed by dividing the number of positive outcomes by the total number of possible outcomes. Here's the formula: $$ProbabilityofaneventP(E)=\frac{Numberofpositiveoutcomes}{Totalnumberofoutcomes}$$ $$HereP(E)=Probabilityofoccuringanevent$$ $$andP(E̅̅̅̅̅̅)=Probabilityofnotoccuringanevent$$ $$RememberalwaysP(E)+P(E̅̅̅̅̅̅)=1$$ For example: 1. If you have two yellow pillows out of six,...

  Hi Friends and Champs!  We will discuss about the median for grouped given data in the upcoming exercise. You were already familiar with finding the median for an ungrouped data from the prior class. To determine the median for ungrouped data, follow these steps: Step-1 Rearrange the given frequency (Data ) in the ascending order. Step-2  If the total of the  given frequency (Data )  is odd then the median is $$\frac{n+1}{2}thobservation$$ otherwise ( if total is even ) the average of the $$\frac{n}{2}+⟨\frac{n}{2}+1⟩thobservations$$  Example for the data as given below:    Observations           Frequency of occurrence           x 1                                                   f 1   ...

Hi Friends and Champs! We will talk about the mode of some supplied grouped data today. Remember that you have already learnt the mode for ungrouped data from the last class. As you are previously aware, the mode for ungrouped data is the frequency that is repeated more frequently. As an illustration: Example - Run score by a batsman in 8 matches are 50,98,99,98,76,75,99,98.Find the mode ? Solution : 98 runs repeated 3 times , Hence mode is 98. It is evident from the example above that figure 98 is the mode because it is repeated three times.Thus, it is easy to find the mode for ungrouped data. However, it is a little more complicated with aggregated data. For ungrouped data, we select the class with the highest frequency and use the formula below to determine the mode. $$Mode=l+\frac{f1-f0}{2f1-f0-f2}\times h$$ where l = lower limit of the modal class, h = size of the class interval (assuming all class sizes to be equal), f1 = frequency of the modal class, f0 = frequency of t...

Hi Friends and Champs! In the next exercise, we will talk about the mean or average for given data. You already learn about the mean for the ungrouped data in the previous class: Example for the data as given below:    Observations           Frequency of occurrence           x 1                                                   f 1           x 2                                                  f 2           x 3                                       ...

Hi Friends and Champs!  In this chapter, we will learn to find the resulting volumes by joining or scooping of different shape bodies in the same way as in previous exercise. Let's start.  Exercise 12.2 1.A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.  Solution: radius of both cone and hemisphere r = 1 cm height of the cone h = r = 1 cm Volume "v" of the solid = volume of the hemisphere + volume of the cone v = 2/3  πr ³ + 1/3  πr ² h =2/3  π1 ³ +   1/3  π1 ² ×1 = 2/3  π +  1/3  π = π cm ³ Ans. 2. Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contai...