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[entobabioty of2 successes each occurring resulting - becoce failures? with probability L what is...

Question

[entobabioty of2 successes each occurring resulting - becoce failures? with probability L what is

[entobabioty of2 successes each occurring resulting - becoce failures? with probability L what is



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Five independent trials of a binomial experiment with probability of success $p=0.7$ and probability of failure $q=0.3$ are performed. Find the probability of each event.
At most one failure

We have a bite on the experiment. With five independent trials and the probability of success and he trial being 0.7 and the probability of failure being a Q is equal to use equal to 0.3, and we're gonna try to find the probability of their being knows. No, um, successes. There is no failure. So no failures, all successes. So all five will be successes. Which means the race was your 50.17 number successes, which is five, and their 0.3 to the zero power is just Once you leave it out, 3.7 to the fifth power can use. Your catheter is about 10.16 feet. 07 So this is the probability of their being all successes in this throughout the five trials of this experiment.

Now, here in this problem, we are talking about a binomial distribution or a binomial experiment, and we want to discuss with the word success means whenever we are dealing with binomial experience. Now, the word success does not necessarily imply that something positive has occurred. It doesn't mean that something good has happened, but rather it means that what you were testing to see happen happened. That's a success corresponds with what we call pete. The probability of success, and what it means is that what we are testing? Yeah. To see if it happened, yeah, actually did happen. Okay, Success corresponds with p the probability of success. And so that means success means that what we are testing to see if it actually did happen and actually do.

And this problem. We have five experiments, probably success and each being 0.7. Probably failure. Big 0.3 were asked if on the failure. It's a probability that we have, at most, two failures. So the previous problem we found the probability of, at most one failure being 0.5 to 8 to two. It's all we have to do is add probability of their being exactly two failures. Exactly two fields, which is your 20.3 races. Second power time, zero points out of race and third power because the other three experiments can only be a successes and multiply by because there to meet many combinations of two failures within the total of five experiments. So five factorial, which is the total number of experiments invited by. And we're gonna turn these exponents and do, if actuals to factorial times three. Factual, really, And this value five factorial divided by three factorial times to factories honoring a multiplied by 0.7 cute unemployed. For since your calculator times 0.3 square is equal to 0.3087 The last thing we do is add the's values together 0.52 eights, 22 plus 0.30 seats. Seven. You can use their calculator for this, and we have about we have 0.83692 as a probability that we have at most two failures.

This problem. We have a bite on the experiment of five independent trials with the success rate of P is equal to 0.7. Probability of success and probably a failure being cues equal to 0.3 gonna find the probability that there is exactly one failure. So failure is 0.3 races, one power multiply. So that means the rate of success We have four successes, raises of four power. And because there could be any number, there could be many combinations of there being four successes. Wrote the five files we use ah, function. See, So true's out of five total. Uh, we're gonna have one failure. So this is equal to five factorial divided by four factorial times. One factory always just wants to leave it out is equal to five. So five times your 50.3 times you're a 0.7 to the fourth power. And when you put this into your calculator, we have the problem of these things. Approximately 0.36 0.36015 The probability that there will be only one failure exactly one


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