Probability of no.

juantheron · 2012-04-28 20:02:15

3 no. are choosen from {1,2,3,..........,8} with replacement, Then find the probability that min of choosen no. is = 3

Given that max. of choosen no. is = 6

bobbym · 2012-04-28 22:24:32

Hi;

anonimnystefy · 2012-04-28 22:36:10

Hi juan

Let's calculate the total number of ways to choose the three numbers such that one is 6 and all of them are smaller.

One number is 6 and the other two numbers are from the interval [1,6] so for both numbers we have 6 possibilities. The total number is 6*6=36.

Of those the number of posibilities when of the other two numbers one is 3 and the other is between 3 and 6 is 4.

The probability is 4/36=1/9.

Nfortunately,my solution doesn't match up with bobbym's so it might be correct and might not.

George,Y · 2012-04-30 19:42:02

choose 3 and choose 6, and choose between 4 and 5, multiplied by number of choosing sequence possibilities

But it is with replacement, so we have to consider 336 and 366

hammana · 2012-05-01 23:38:31

Hi

Hereis another way to see things:
There are 8^3 arrangements with repetition of the digits 1 to 8 , 3 by 3
The arrangements 3 by 3 of the digits 3,4,5,6 containing at least once the digits 3 and 6 are:

3-6-x;   6-3-x;  3-x-6;  6-x-3;   x-3-6;   x-6-3

x being any digit 3 to 6 included. The total makes 24; the answer would be 24/8^3=3/64
Who knows where is the truth ?

bobbym · 2012-05-01 23:51:08

Hi;

Who knows where is the truth ?

See post #2.

anonimnystefy · 2012-05-01 23:52:18

How do you know you answer is correct,bobbym?

bobbym · 2012-05-01 23:53:46

You should not have to ask that question. You know that before I do a combinatorics problem I start with the answer first and work backwards.

anonimnystefy · 2012-05-01 23:57:07

But the question is not clear,so it is not possible to know the right answer without further clarification.

bobbym · 2012-05-01 23:58:41

Nope, that is not correct. There is a definite way to know the answer. Then you can back engineer a reasonable math solution.

anonimnystefy · 2012-05-02 00:01:06

It is unclear if all the numbers picked must be less than 6 or only the ones we count.

bobbym · 2012-05-02 00:08:02

An assumption does have to be made on the problem. I have been waiting for juan but he sometimes does not come back to a thread.

Math Is Fun Forum

#1 2012-04-28 20:02:15

Probability of no.

#2 2012-04-28 22:24:32

Re: Probability of no.

#3 2012-04-28 22:36:10

Re: Probability of no.

#4 2012-04-30 19:42:02

Re: Probability of no.

#5 2012-05-01 23:38:31

Re: Probability of no.

#6 2012-05-01 23:51:08

Re: Probability of no.

#7 2012-05-01 23:52:18

Re: Probability of no.

#8 2012-05-01 23:53:46

Re: Probability of no.

#9 2012-05-01 23:57:07

Re: Probability of no.

#10 2012-05-01 23:58:41

Re: Probability of no.

#11 2012-05-02 00:01:06

Re: Probability of no.

#12 2012-05-02 00:08:02

Re: Probability of no.

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