n<- 13
p<-0.7
dbinom(6,size = n, prob = p)
## [1] 0.0441524
x<-0:n
plot(x,dbinom(x,size = n, prob = p), main = "probability mass function of Bin(13,0.7)")

#binomial
pbinom(9,size = n, prob = p)  
## [1] 0.5793944
plot(x,pbinom(x,size = n, prob = p), main = "probability mass function of Bin(13,0.7)")

dbinom(6, size = n, prob = p)
## [1] 0.0441524
x<-0:n
plot(x,dbinom(x,size = n, prob = p), main = "probability mass function of Bin(13,0.7)")

#probability of getting 26 or less heads from a 51 tosses of a coin.
x<- pbinom(26,51,0.5)
x
## [1] 0.610116
plot(pbinom(0:26,51
            ,0.5,1/2), main = "probability mass function of Bin(26,51,0.5)")

#How many head will have a probability of o.25 will came out when a coin is tossed 51 times.
x<-qbinom(0.25,51,1/2)
x
## [1] 23
#Find 8 random values from a sample of 15 wit




#Suppose there are twelve multiple choice question in English class quiz. Each question has
#five possible answers, and only one of them is correct.Find the probability of having four or 
#less correct answers if a student attempts to answer every question at random.

pbinom(4,size = 12, prob = 1/5)
## [1] 0.9274445
#Suppose there are twelve multiple choice question in English class quiz. Each question has
#six possible answers, and only one of them is correct.Find the probability of having six or 
#less correct answers if a student attempts to answer every question at random.

pbinom(5,size = 12, prob = 1/6)
## [1] 0.992075
#In a large restaurant an average of 3 out of 5 customer ask for water with their meal.
#A random sample of 10 customer is selected
#A) FIND THE PROBABILITY THAT (i)exactly 6 ask for water with their meal,
#(ii) less than 9 ask for water with their meal.

#(i) answer
dbinom(6,size = 10, prob = 3/4)
## [1] 0.145998
#(ii) ans
pbinom(9,size = 10, prob = 3/4)
## [1] 0.9436865
#A homeowner plants 6 bulbs selected at random from a box containing 5 tulip bulbs and 4 daffodil
#bulbs. What is the probability that he planted 2 daffodil bulbs and tulip bulbs?
dhyper(x=2,m=4,n=5,k=6)
## [1] 0.3571429
#A storeroom just received a shipment of 13 paper grates. Shortly after they were received, the 
#manufacturer called to report that he had inadver tently shipped 5 defective units. The owner of 
#the owner of the storeroom decided to test 4 of the 13 paper graters she received. Assume

#3 or less unit defective
phyper(q=3,m=5,n=8,k=4)
## [1] 0.993007
#more than 2 unit are defector
phyper(q=2,m=5,n=8,k=4, lower.tail = FALSE)
## [1] 0.1188811
#A Company produces and ships 16 personal computers knowing that 5 of them have defective wiring.
#The company that purchased the computers is going to thoroughly test four of the computers. The 
#purchasing company can detect 



#A CD contains 10 songs; 6 are classical and 4 are rock and roll. in a sample of 3 songs, what is the 
#probability that exactly 2 are classical? Assume the samples are drawn without replacement.
dhyper(x=2,m=6,n=4,k=3)
## [1] 0.5

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