algebra 1

Given any random, 3-digit number, what is the
probability that a number will be:
a) a multiple of 5
b) divisible by 2
c) a square number

i know the answer but i don't know how to solve it

  1. 👍 0
  2. 👎 0
  3. 👁 116
asked by naomi
  1. when you divide a number by 5, there are only 5 possible remainders: 0,1,2,3,4. So, since multiples of 5 have zero remainder, there's a 1/5 chance that a random number will be a multiple of 5.

    In fact, there's a 1/n chance that a number will be a multiple of n.

    For the squares, you need to figure out how many perfect squares there are between 100 and 999. If there are, say, 35, then there's a 1/35 chance that a random 3-digit number will be a square.

    1. 👍 0
    2. 👎 0
    posted by Steve
  2. number of 3-digit numbers :
    999-99 = 900

    multiples of 5:
    5, 10, 15, ... , 995 ---> 199 of them

    prob(multiple of 5) = 199/900

    divisible by 2 --- > must be even
    numbers are :
    100, 102, 104, ... 998 ----> 445 of them
    prob(even) = 445/900 = 89/180

    numbers which when squared produce a 3 digit number
    10^2 = 100
    11^2 = 121
    ..
    31^2 = 961
    32^2 = 1024 ... too large
    so there are 22 of these 3-digit squares
    prob(square) = 22/900
    = 11/450

    I hope you know how I am getting these counts.
    e.g. how many even numbers from 100 to 998
    consider them to be an arithmetic sequence
    where a = 100 , d = 2 and t(n) = 998
    a + (n-1)d = term(n)
    100 + (n-1)(2) = 998
    2(n-1) = 898
    n-1 = 449
    n = 449+1 = 450

    1. 👍 0
    2. 👎 0
    posted by Reiny
  3. Take Reiny's analysis. He paid a bit more attention to the details than did I.

    1. 👍 0
    2. 👎 0
    posted by Steve
  4. but the answer is 96

    1. 👍 0
    2. 👎 0
    posted by da
  5. "what is the probability" ...
    cannot have 96 as the answer.

    1. 👍 0
    2. 👎 0
    posted by Steve
  6. ok thanks

    1. 👍 0
    2. 👎 0
    posted by da

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A 3-digit positive integer is selected at random. Find the probability that A) The last two digits of the number is 22 B) The number is greater than 900 C) The number is less than 100 D) The number contains at least one digit 8

    asked by Ledyyyy on February 13, 2016
  2. stats

    In a straight 3 lottery you choose a 3 digit number. A 3 digit number is chosen at random, If your number mataches you win $250. 1. There are two outcimes in the sample space($250,$0) using these write down a probability model for

    asked by Morgan on October 7, 2017
  3. probability

    please help! 1.) A random digit from 1 to 9 (inclusive) is chosen, with all digits being equally likely. The probability that when it's squared it will end with the digit 1. 2.) A random number between 1 and 20 (inclusive) is

    asked by karen on August 11, 2012
  4. math

    please help! 1.) A random digit from 1 to 9 (inclusive) is chosen, with all digits being equally likely. The probability that when it's squared it will end with the digit 1. 2.) A random number between 1 and 20 (inclusive) is

    asked by karen on August 11, 2012
  5. MATH

    Jason remembers nine digits of a ten digit phone number. He remembers that the last digit is an even number. If he guesses that last digit, what is the probability that he dials the correct number? My answer: 1/5 probability

    asked by Pleasecheckmyanswer on March 24, 2016
  6. Statistics

    A two-digit number is written down at random.Find the probability that the number will be A)Smaller than 20 B)Even C)Multiple of 5

    asked by Rukhsar on January 4, 2017
  7. kv luchnow

    one of two digit of a two digit number is 5 time other digit if we interchange the digit of is two digit number the resulting new number is 6 more then thrice theoriginal number find two digit original two digit number

    asked by juni on September 7, 2015
  8. Maths

    3. A three digit number is selected at random. What is the probability that its unit digit is 2

    asked by Shahistha on November 27, 2016
  9. math

    How many digit number greater than 200 but less than 300 can be obtained from 1234,and what is the probability that a number choosen at random falls into this range

    asked by Yinka on June 6, 2012
  10. Probability please help!

    The digits 2, 3, 4, 7, and 8 are each used once in a random order to form a five-digit number. What is the probability that the resulting number is divisible by 4? Express your answer as a common fraction.

    asked by SuckatProb on November 20, 2012

More Similar Questions