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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 ...

Question

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.Exactly three successes

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. Exactly three successes



Answers

Binomial Trials Five independent trials of a binomial
experiment with probability of success $p=0.7$ are performed.
Find the probability of each event.
Exactly three successes

Okay, so we've got binomial experiment with five intimate and trials. The probability of success is 0.7. And so we're going to calculate what is the probability when we have no successes. So then we're going to have five Choose zero, which is going to look exactly like this. You're a factorial five factorial. And so then this is just going to be one, and then we're gonna have 0.7 to the zeroth power, which is again, just gonna be one, and then we'll have a 0.3 to the fifth. So once we calculate with point three to the fifth is it's going to be this very small number 0.0 0243 We've got our answer.

So we're looking for the probability of this binomial experiment with five independent trials with probability success of 0.7 and we're looking for the probability that we have all successes. So we're gonna have 5 to 5, which is going to just be this, which is just gonna be one. And we'll have 0.7 to the fifth and 0.3 to the zeroth power, which is again just one. So we'll do 0.7 to the fifth, which is equal to zero point 16 807

Okay, so we have a binomial experiment with five trials, and the success chance is 0.7, and we're looking for the chance of getting exactly one success, which is going to look like this. This is our five choose for which is just gonna end up being five, and we'll have a 0.7. This is for exactly one success. So this is going to be the the one power, then what? 0.3 to the fourth. So if we d'oh 0.3 to the fourth, we end up getting to your 0.0 81 time, 0.7 times five times point your time. 2.7 times five. We get this equal to 0.0 2835 for our finally

Okay, so we're doing a binomial experiment with five independent trials with the success chance being 0.7. And we want to find the probability that we get exactly one failure, which is the same as saying we get exactly four successes. So for in choose, our will have five choose four, which would just be the same is doing this here, which is going to give us five and will have 0.7 to the fourth. We'll have our 0.3 which guns? From one minus 0.7 to the one power. That's gonna give us five times 50.7 to the fourth, which is equal to 0.2401 time 0.3. When we multiply all that out, we end up getting no 0.36 0 15 Let's make sure, actually, looks kind of like a zero


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