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anonymous
 4 years ago
Assume 3 digits are selected at random from the set (1,2,3,7,8,9) and are arranged in random order. What is the probability that the resulting 3 digit number is less than 700?
anonymous
 4 years ago
Assume 3 digits are selected at random from the set (1,2,3,7,8,9) and are arranged in random order. What is the probability that the resulting 3 digit number is less than 700?

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Directrix
 4 years ago
Best ResponseYou've already chosen the best response.2Fine until I saw this problem. :) Just kidding, CW.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ha i have tons of them....

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.2Find out how many different numbers you can make out of the three digits, and how many of those are less than 700. There are 6*5*4=120 ways to make a three digit number out of the 6 given digits. Out of these, if we were to make a number less than 700, the first digit must be less than 7 (three choices), the remaining digits have 5 and 4 choices for a total of 3*5*4=60 ways. So probability P(<700)=N(<700)/N(all)

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.2N(all) is 6*5*4=120 ways with no restrictions.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0what would the probability be then?

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.2So probability P(<700)=N(<700)/N(all)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0im still not sure how this answer is supposed to look

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.2There are 60 (desirable) ways to make 3digit numbers less than 700 out of 120 (possible) ways to make 3digit numbers out of the given 6 distinct digits. So the probability required, P(<700) is given by P(<700) = number of desirable events / number of possible events.

Directrix
 4 years ago
Best ResponseYou've already chosen the best response.2We are making 3digit numbers that are less than 700. So, the first digit of the 3digit number cannot be 7, 8, or 9. For the first digit, we have 3 choices (1,2, or 3). After selecting one of (1,2,3) for the first digit, there are 5 choices left for the number's second digit, and then 4 choices for the third digit. By the Fundamental Principle of Counting, there are 3 times 5 times 4 = 60 ways to make a 3digit number less than 700 from the given digits. 60 is the desired number of outcomes. For the probability denominator, we need the number of possible outcomes of the formation of the 3digit number. That would be 6 times 5 times 4 or 120. The probability of creating a 3digit number less than 700 from the digits 1,2,3,7,8,9 is 60/120 or 1/2.

Directrix
 4 years ago
Best ResponseYou've already chosen the best response.2Sorry, CW, I had to stop eat, and then the server threw me off. I'm back now.

Directrix
 4 years ago
Best ResponseYou've already chosen the best response.2CW, did you see my work here? Do you agree?

mathmate
 4 years ago
Best ResponseYou've already chosen the best response.2@cw Yes, 1/2 is correct. Directrix explained everything in detail. Hope you will benefit from his excellent efforts.
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