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mathmath333
 one year ago
Probablity question
mathmath333
 one year ago
Probablity question

This Question is Closed

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} & \normalsize \text{Three different numbers are selected from the set}\ X=\{1,2,3,4...10\}\hspace{.33em}\\~\\ & \normalsize \text{What is the probablity that the product of the two numbers is equal to }\hspace{.33em}\\~\\ & \normalsize \text{the third }\hspace{.33em}\\~\\ \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} & a.)\ \dfrac{3}{10}\hspace{.33em}\\~\\ & b.)\ \dfrac{1}{40}\hspace{.33em}\\~\\ & c.)\ \dfrac{1}{20}\hspace{.33em}\\~\\ & d.)\ \dfrac{4}{5}\hspace{.33em}\\~\\ \end{align}}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2say the \(3\) numbers selected are \(\{a,b,c\}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2also suppose that \(a\lt b\lt c\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2then you want \(a*b\le 10\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2notice that if \(a*b\le 10\), then \(a \le \sqrt{~10~}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2so \(a\) can only be either \(2\) or \(3\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2when \(a=2\), check what all \(b\) values will work

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1how does the condition \(a=\sqrt{10}\) came.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2good question, that is called seive of eratosthenes https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2we have \(ab\le 10\) and you know that \(a\lt b\) whats the maximum value that \(a\) can take ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1cuz \(3\times 4=12\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Perfect! so the only value that \(a\) can take is \(2\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2remember you want to pick all 3 "different" numbers

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2what happens if any one number is \(1\) ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1it satisfies the condition example \(1,2,3\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2it doesn't, 1*2 is not 3

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2the smaller two numbers must multiply to the third number

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1yea , only \(2\) for \(a\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yes let \(a=2\) and find all \(b\) such that \(a*b\le 10\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, so the numbers in favor are : (2, 3, 6) (2, 4, 8) (2, 5, 10)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2next, find how many total ways are there to choose 3 different numbers from the given 10 numbers

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1Is their any condition to choose 3 different numbers from the given 10 numbers.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2thats the sample space so no conditions, just find the total number of ways of choosing 3 numbers from 10

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\dfrac{10!}{7!}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2its just \(\large \dbinom{10}{3}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2notice that here order doesn't matter... so it is a combination

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1why not \(^{10}P_{3}\) ??

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2favor : \(\large 3\) total : \(\large \dbinom{10}{3}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2take the ratio for the probability

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1so answer=\(\dfrac{1}{40}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Yes, did u get why this is a combination and not a permutation problem ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1cuz we choosing 3 numbers one by one and not forming 3 numbers like \(abc_{10}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2yes, we never bothered about order while doing this problem

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2we could also do it using permutations but it is painful here

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2if we use permutations, the count of favor also changes

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2(2, 3, 6) (2, 4, 8) (2, 5, 10)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2since (2, 3, 6) works, all the 6 permutations of it also work : (2, 6, 3) (3, 2, 6) (3, 6, 2) (6, 2, 3) (6, 3, 2)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2after all that mess, you will get the same answer

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2In these probability problems, it doesn't matter whether you use permutations or combinations.. the final answer wont change if you do it correctly
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