Bernoulli probability: prob success in 2 trials 0,39; prob success in 3 trials 0,43

[anonymous2]

I have to calculate the probability of 1 success in 3 trials.

The probability of one success in one trial is 0,27.
I used Bernoulli pattern to calculate it and that what I got below. I assume I can't use it properly or I don't understand something.

The probability of success in two trials is 0,39
The probability of success in three trials is 0,43

The probability of success in ten trials is 0,16 !!!????
The probability of 2 successes in ten trials is 0,26 ??? how that's possible?

I don't understand, if 3 trials gives 0,43, so 10 trials should be about 1 or above (in my opinion). Thank you in advance for explanation.

 

[stapel]

I have to calculate the probability of 1 success in 3 trials.

The probability of one success in one trial is 0,27.
I used Bernoulli pattern to calculate it and that what I got below.

Are you using the following?

. . . . .\(\displaystyle {}_n C_r\, p^r\, q^{n-r}\)

...where "n" is the number of trials, "r" is the exact number of successes, "p" is the probability of success in any one trial, and "q" is the probability of failure in any one trial. (here) Note that this returns the probability of exactly r successes in n trials, not "at least" r successes!

I assume I can't use it properly or I don't understand something.

The probability of success in two trials is 0,39
The probability of success in three trials is 0,43

The probability of success in ten trials is 0,16 !!!????
The probability of 2 successes in ten trials is 0,26 ??? how that's possible?

You have computed the probability of exactly two successes in ten trials. If you meant to compute the probability of at least two successes, then you need to compute the probabilities of exactly two successes, plus the probability of exactly three successes, plus the probability of exactly four successes, ..., plus the probability of exactly ten successes. (here) Or, which is easier, find the probability of exactly zero successes plus the probability of exactly 1 success; then subtract this sum from "1".

I don't understand, if 3 trials gives 0,43, so 10 trials should be about 1 or above (in my opinion).

How do you figure that any result would have a probability of greater than 100% of occurring? :shock:

 

[anonymous2]

Are you using the following?

. . . . .\(\displaystyle {}_n C_r\, p^r\, q^{n-r}\)



You have computed the probability of exactly two successes in ten trials. If you meant to compute the probability of at least two successes, then you need to compute the probabilities of exactly two successes, plus the probability of exactly three successes, plus the probability of exactly four successes, ..., plus the probability of exactly ten successes. (here) Or, which is easier, find the probability of exactly zero successes plus the probability of exactly 1 success; then subtract this sum from "1".

I can't understand that

The probability of success in ten trials is 0,16
The probability of 2 successes in ten trials is 0,26

If I want to get one success in 10 trials then probability is lower than for 2 successes? That's contradiction for me. That's what I can't understand

 

[stapel]

I can't understand that

The probability of success in ten trials is 0,16
The probability of 2 successes in ten trials is 0,26

If I want to get one success in 10 trials then probability is lower than for 2 successes? That's contradiction for me. That's what I can't understand

There is a big difference between "exactly" (which you have computed, and which means "no more than, and no less than") and "at least" (which means "exactly this, plus every option greater than this"). Until you do the computation for "at least 2", you will get only the result for "only and exactly 2", which obviously is going to be less than "2, or 3, or 4, or ..., or 9, or 10". Same with "exactly 1" (which is hard to get, so the probability will be low) and "at least 1", which means "1, or 2, or 3, or... or 9, or 10".

You're computing "=", and you're wondering why the results aren't matching your expectations for ">". They're not matching because they're not the same thing.

 

[anonymous2]

thank you.

 

[anonymous2]

so how to get what I want to get? where I can find this material

 

[anonymous2]

There is a big difference between "exactly" (which you have computed, and which means "no more than, and no less than") and "at least" (which means "exactly this, plus every option greater than this"). Until you do the computation for "at least 2", you will get only the result for "only and exactly 2", which obviously is going to be less than "2, or 3, or 4, or ..., or 9, or 10". Same with "exactly 1" (which is hard to get, so the probability will be low) and "at least 1", which means "1, or 2, or 3, or... or 9, or 10".

You're computing "=", and you're wondering why the results aren't matching your expectations for ">". They're not matching because they're not the same thing.

Well, so how to get the result? Sorry for that, but I'm on elementary level, it is quite difficult for me and also quite important. I got a book about this subject but I need some time. Thank you.