How many positive three-digit integers are multiples of 6?

(b) what is the probability that a randomly chosen positive three-digit integer is a multiple of 6?

(c) what is the probability that a randomly chosen positive three-digit integer is a multiple of 7?

Answer with Step-by-step explanation:

a.Three digit number which is multiple of 6

102,108,...996

a=102,

d=108-102=6

It is an A.P because the difference between two consecutive terms is constant.

nth term of A.P is given by

Substitute the values then we get

Numbers of positive three-digit integers which are multiple of 6=150

b.Three digits number lying between 100 and 999 therefore,

Total three digit positive integers=

Probability,P(E)=

The probability that a random chosen positive three- digit integer is a multiple of 6=

c.Positive integers of multiply of 7 are

105,112,119,....,994

d=112-105=7

Using nth term of A.P formula

The probability that a random chosen positive three digit integer is a multiple of 7=

-1/2 +2

step-by-step explanation: