Where is my logic wrong (lottery problem)

[r0bHadz]

Homework Statement

Find the probability of selecting exactly one of the correct
six integers in a lottery, where the order in which these
integers are selected does not matter, from the positive
integers not exceeding 40

Relevant Equations

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. -google

I don't understand why I can't answer this question as a bernuli trial.

There are 6 possible correct integers out of 40, and 34 incorrect integers out of 40. I'd assume it would look like this:

(6c1)(6/40)(34/40)^5

I guess, it's because when you choose and incorrect or correct integer, the probability of getting a correct/incorrect integer changes? meaning this part: "in which the probability of success is the same every time the experiment is conducted." of the equation is not satisfied? Does my reason for why this doesn't work make sense?

 

[PeroK]

I don't understand why I can't answer this question as a bernuli trial.

There are 6 possible correct integers out of 40, and 34 incorrect integers out of 40. I'd assume it would look like this:

(6c1)(6/40)(34/40)^5

I guess, it's because when you choose and incorrect or correct integer, the probability of getting a correct/incorrect integer changes? meaning this part: "in which the probability of success is the same every time the experiment is conducted." of the equation is not satisfied? Does my reason for why this doesn't work make sense?

You have to pick a different number each time. There are, therefore, only 39 possibilities for your second number etc.

 

[r0bHadz]

Hmm gotcha. So because the probability of success is not the same each time, this can't be a bernouli trial.

 

[LCKurtz]

Order isn't really relevant in this problem. You have two subsets, the 6 winners and the 34 losers. You want 1 from the set of 6 and 5 from the set of 34. The hypergeometric distribution is appropriate. See:
http://mathworld.wolfram.com/HypergeometricDistribution.html

 

[PeroK]

Hmm gotcha. So because the probability of success is not the same each time, this can't be a bernouli trial.

Yes, your answer would be correct if You could pick the same number more than once.

 

[r0bHadz]

Order isn't really relevant in this problem. You have two subsets, the 6 winners and the 34 losers. You want 1 from the set of 6 and 5 from the set of 34. The hypergeometric distribution is appropriate. See:
http://mathworld.wolfram.com/HypergeometricDistribution.html

Nice! this problem is actually from a discrete math book, and I'm taking a probability course right now, and we haven't learned about hypergeometric distribution surprisingly.

 

[WWGD]

You have 5 spaces for the wrong one, 34 numbers to choose those spaces.

 

[kristanmrk]

Problem Statement: Find the probability of selecting exactly one of the correct
six integers in a lottery, where the order in which these
integers are selected does not matter, from the positive
integers not exceeding 40
Relevant Equations: In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. -google

I don't understand why I can't answer this question as a bernuli trial.

There are 6 possible correct integers out of 40, and 34 incorrect integers out of 40. I'd assume it would look like this:

(6c1)(6/40)(34/40)^5

I guess, it's because when you choose and incorrect or correct integer, the probability of getting a correct/incorrect integer changes? meaning this part: "in which the probability of success is the same every time the experiment is conducted." of the equation is not satisfied? Does my reason for why this doesn't work make sense?

Agree with your comparison and update. Everything is in the probability then one who know the true way always win this game