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setwd("C:/Users/jains/Desktop/Vit Pune/Sem 2/Labs/Data Science/Lab 2")

travel = read.csv("travelled_abroad_data.csv")
attach(travel)

#1.	Find out the % of Indians in the sample 
#   who have traveled abroad using the data source

yesTravel = sum(Travelledabroad == "Y")
per1 = ((yesTravel / length(Sr..No.)) * 100)
per1

notTravel = sum(Travelledabroad == "N")
per2 = ((notTravel / length(Sr..No.)) * 100)
per2


#2.	Treating this value as "p" , calculate the following probabilities

#   a. What is the probability that in a 
#      randomly chosen sample of 10 persons, no one has traveled abroad.


1 - pnorm(66, mean=1, sd=10, lower.tail =TRUE, log.p = F)

#  b.	What is the probability that in a randomly chosen sample of 
#     10 persons, exactly one has traveled abroad.

1 - pnorm(84, mean=9, sd=10, lower.tail =TRUE, log.p = F)

#c.	What is the probability that in a randomly chosen sample of 10 persons,
#   exactly two persons have traveled abroad.

1 - pnorm(84, mean=8, sd=10, lower.tail =TRUE, log.p = F)

#d.	What is the probability that in a randomly chosen sample of 10 persons,
#   exactly three persons have travelled abroad.

1 - pnorm(84, mean=7, sd=10, lower.tail =TRUE, log.p = F)

#e.	What is the probability that in a randomly chosen sample of 10 persons,
#   exactly four persons have travelled abroad.

1 - pnorm(84, mean=6, sd=10, lower.tail =TRUE, log.p = F)

#f.	What is the probability that in a randomly chosen sample of 10 persons,
#   exactly five persons have travelled abroad.

1 - pnorm(84, mean=5, sd=10, lower.tail =TRUE, log.p = F)

#g.	What is the probability that in a randomly chosen sample of 10 persons, 
#   exactly six persons have travelled abroad.

1 - pnorm(84, mean=4, sd=10, lower.tail =TRUE, log.p = F)

#h.	What is the probability that in a randomly chosen sample of 10 persons, 
#   exactly seven persons have travelled abroad.

1 - pnorm(84, mean=3, sd=10, lower.tail =TRUE, log.p = F)

#i.	What is the probability that in a randomly chosen sample of 10 persons, 
#   exactly eight persons have travelled abroad.

1 - pnorm(84, mean=2, sd=10, lower.tail =TRUE, log.p = F)

#j.	What is the probability that in a randomly chosen sample of 10 persons, 
#   all 10 persons have travelled abroad.

1 - pnorm(84, mean=1, sd=10, lower.tail =TRUE, log.p = F)



# 3.	Plot the probability values as a Table / Bar graph and interpret

table(travel$Travelledabroad == "Y", travel$Travelledabroad == "N")

# 4.	What is the probability that in the randomly chosen sample of 100 persons
#  at least 59 have travelled abroad? 

pnorm(84, mean=59, sd=100, lower.tail =TRUE, log.p = F)