Solved Problems-III:Probability Theory

Q1: There are 3 groups of children, containing 3 girls and 1boy, 2 girls and 2 boys, 1 girl and 3 boys respectively. One child is selected at random from each group. Find the probability of selecting 1 girl and 2 boys. Solution: Let G be the event of selecting girl Let B be the event of selecting boy Different cases and associated probabilities are given below: Case1: Group1: G, Group2: B, Group3: B - Probability = ¾ x 2/4 x ¾ Case 2: Group1: B, Group2: G, Group3: B - Probability =…continue reading →

Solved Problems-II:Probability Theory

Q1: A box of chocolates contain 3 orange, 5 green and 6 red chocolates. If one is taken at random, what is the probability that it is either orange or red? Solution: Total number of chocolates = 14 Favourable cases = 9 Hence answer = 9/14 Q2: A box of chocolates contain 4 orange, 5 green and 6 red chocolates. If 2 chocolates are taken at random, what is the probability that : Both are red One is green and one is orange Solution: Total number of chocolates = 15 Number of ways…continue reading →

Solved Problems-I: Probability Theory

Q1: Find the probability that a leap year selected at random will contain 53 Sundays. solution : A leap year contains 366 days which include 52 complete weeks and two additional days. These two days can be: (1). Monday and Tuesday ,(2). Tuesday and Wednesday, ... and so on. Of these 7 possibilities only 2 contain a Sunday. Hence probability that a leap year has 53 Sundays = 2 / 7 Q2: Two dice are rolled. Find the probability that both the dice show the same number Solution: 6 / 36 = 1…continue reading →
IOT Setup Using ESP8266 and HiveMQ Public MQTT

IOT Setup Using ESP8266 and HiveMQ Public MQTT

  This is a basic Internet of Things (IOT) project using a public MQTT server. I am doing two things here: Control an LED at my home from anywhere in the world, by simply publishing an “on” or “off” command in the browser. Read the temperature inside my room from the browser, wherever I go. Watch a video on NodeMCU and HiveMQ: Following components are used for this project: NodeMCU (an ESP8266 based SoC board), usually used for IOT projects A temperature sensor (LM35) Onboard LED on NodeMCU, that is connected to pin…continue reading →

Properties and Theorems on Probability

Properties (1) ; where denotes the null set. We have By probability axiom, Therefore, (2) If A is an event and is its complement, then, We have = S Therefore,   Note: If P(E) = 1, then E is called a sure event and if P(E) = 0, then E is called an impossible event. Addition theorem on 2 events If A and B are any two events, then Note: If A and B are mutually exclusive, Then So, Addition theorem for 3 events If A,B and C are any three events, Note:…continue reading →

Defining Probability

There are three approaches to defining probability Mathematical or Classical Empirical Axiomatic Mathematical or Classical Definition of probability If there are n exhaustive mutually exclusive and equally likely cases, of which m cases are favourable to the happening of an event A, then the probability of A is defined as   Clearly, Examples: Probability of getting H in a coin toss experiment = Probability of getting 6 in a die rolling experiment = Probability of drawing a spade from a deck of 52 cards = Empirical Definition of Probability The mathematical definition of…continue reading →
Arduino powered Remote Controlled Car

Arduino powered Remote Controlled Car

This project note may be a very interesting one for you. It is a remote controlled (RC) car made using an Arduino UNO. Here are some demo videos List of materials Hardware Arduino Uno L293D motor driver board HC-05 bluetooth module Chassis and wheels for the car Some jumper wires A battery pack A computer for programming the Arduino Software Arduino IDE -- arduino.cc/Downloads The android app to controll the car -- https://play.google.com/store/apps/details?id=braulio.calle.bluetoothRCcontroller Arduino is a platform which is very useful for creating many electronics projects. The HC-05 is a bluetooth tranceiver module.…continue reading →
Events

Events

As discussed in the previous posts, a random experiment will have multiple possible outcomes. While conducting an experiment, we may be interested not just in one outcome, but in a set of outcomes. For example, in the experiment of rolling a die, the event of getting an odd numbered face represents a set of possible outcomes :- set   Similarly, the event of getting an even numbered face is another set of possible outcomes :- set It must be noted that, the above defined sets  and   are subsets of the sample space…continue reading →
Introducing Probability

Introducing Probability

The term “probability”, is used in our everyday life, to denote the degree of belief in a particular outcome of an experiment. Some examples: The chance for a candidate to win the election The probability of getting stuck in a traffic jam during the morning hours The chance for a defective part to come out of the assembly line, in a batch of 1000 Random Experiment An experiment or trial having more than one possible outcome is referred to as a random experiment. Outcomes of such experiments cannot be predicted with certainty. In the…continue reading →