SOLUTION: 1. Four hundred people attending a party are each given a number, 1 to 400, for a door-prize drawing. One number is drawn at random to determine the winner. Find the probability

Question 338700: 1. Four hundred people attending a party are each given a number, 1 to 400, for a door-prize drawing. One number is drawn at random to determine the winner. Find the probability that the number drawn:
a. is 123

b. Consists of the same three digits.

c. has two digits and ends in 9

d. does not contain an 8

e. is an even number or greater than 390.

Found 2 solutions by stanbon, nyc_function:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Four hundred people attending a party are each given a number, 1 to 400, for a door-prize drawing. One number is drawn at random to determine the winner. Find the probability that the number drawn:
a. is 123 ::::::: 1/400
------------------------------
b. Consists of the same three digits.
There are 6 such numbers: 111,222,333
Probability = 3/400
----------------------------
c. has two digits and ends in 9
1st digit: 3 ways: 1,2,3
2nd digit: 10 ways: 0-9
3rd digit: 1 way: 9
---
3*10*1 = 30/400 = 3/40
d. does not contain an 8
1st digit: 3 ways: 1,2,3
2nd digit: 9 ways: 0,1,2,3,4,5,6,7,9
3nd digit: 9 ways: 0,1,2,3,4,5,6,7.9
----
(3*81)/400 = 243/400

e. is an even number or greater than 390.
P(even) + P(>390) - P(even and >390)
1st: 1,2,3
2nd: any of 10
3rd: ends in 2,4,6,8,0
--
>390: 391-400
[3*10*5 + 10 - 5]/400 = 155/400
====================================
Cheers,
Stan H.

Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
a/. There is only one number out of 400 that is equal to 123, so the probability the number drawn is 123 is 1/400
b/. What numbers less than 400 are three digit numbers, where each digit is the same? There's 111. 222 and 333, three numbers, so the probability the number consists of the same three digits is 3/400.
c/. What two digit numbers are there that end in 9? 19, 29, 39, 49, 59, 69, 79, 89, 99. Nine of them, so the probability the number has two digits ends in 9 is 9/400.
d/. In any given set of 100 numbers there will be 10 that have an 8 in the tens digit. There will also be 10 numbers that have an 8 in the units digit. So there are 20 numbers that contain an 8. Are there? No, there is one number that has an 8 in both the tens and 1 digits, so there will only be 19 numbers in each set of 100 that contain an 8. So there will be 81 out of every hundred that do not contain an 8, and therefore the probability the number drawn does not have an 8 is 81/100.
e/. Exactly half the numbers will be even, so there will be 200 even numbers. There will also be 10 numbers greater than 390. But careful, there are 5 numbers that are both even and greater than 390, namely 392, 394. 396, 398, 400. So there will be 205 numbers either even or greater than 390, and therefore the probability the drawn number is even or greater than 390 is 205/400, which simplifies to 41/80.

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