Question

An integer is selected at random from the set {1,2,3...1000}. What is the probability that it is divisible by 4,5,or 6?

Answer 1

The sample space is

S={1,2,3,.....,998,999,1000}

n(S)=1000

Let A denotes number which are divisible by 4,5 or 6

A={4,5,6,8, 10 ,12 ,15 , 16,......,966 , 968 , 970, 972, 975, 976 ,978 , 980 , 984 , 985 , 988 , 990, 992 , 995, 996, 1000}

n(A)=466

The probability that it is divisible by 4,5,or 6 is

P(A)=n(A)/n(S)=466/1000=0.466

The probability that it is divisible by 4,5,or 6 is 0.466

The R-code is

x=1:1000

A=length(which(x%%4==0|x%%5==0|x%%6==0))

N=length(x)

A #Total number which are divisible by 4,5 or 6

[1] 466

N # Total number of observations

[1] 1000

#Now probability that the number from integer {1,2,...,1000} which is divisible by 4 or 5 or 6 is

A/N

[1] 0.466