SOLUTION: An integer from 100 through 999, inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit? a) 19/900 b) 81/900

Question 256025: An integer from 100 through 999, inclusive, is to be chosen at random. What is the probability that the number chosen will have 0 as at least 1 digit?
a) 19/900 b) 81/900 c) 90/900 d) 171/900 e) 271/900
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
FIrst we have to find the total number of integers in the set: 999-100+1 = 900.
Next we need an organized way to determine our successful options: 0 in at least 1 digit.
0 in 3 digits:
0
0 in 2 digits:
100, 200, 300, 400, 500, 600, 700, 800, 900 = 9
0 in 1 digit:
101 - 110, 120, 130, 140, . . ., 190: 18
201 - 210, 220, 230, 240, . . ., 290: 18
. . .
901-910, 920, 930, 940, . . . 990: 18
or 18*9 = 162
Now 0 +9 + 162 = 171
So the probability is
171/900 = 19/100
RELATED QUESTIONS
an integer from 100 through 999 inclusive, is to be chosen at random. What is the... (answered by stanbon)

an integer from 100 through 999 inclusive, is to be chosen at random. What is the... (answered by jim_thompson5910)

If three numbers from 100 to 999 are chosen at random, one at a time, find the... (answered by ikleyn)

If three numbers from 100 to 999 are chosen at random, one at a time, find the... (answered by Edwin McCravy)

Let an integer be chosen at random from the integers 1 to 30 inclusive. Find the... (answered by Fombitz)

A number is chosen at random from 1 to 600 inclusive. What is the probability that it... (answered by math_tutor2020)

An integer is selecred at random from among all the integers between 100 and 999,... (answered by Edwin McCravy)

Two integers (from 1 to 30, inclusive) are chosen by a random number generator on a... (answered by stanbon)

an integer between 3 and 12 inclusive is chosen at random,what is probability that it is... (answered by josgarithmetic)