yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Probability for a geometric random variable | Random variables | AP Statistics | Khan Academy


2m read
·Nov 11, 2024

Jeremiah makes 25% of the three-point shots he attempts, far better than my percentage for warmup. Jeremiah likes to shoot three-point shots until he successfully makes one. All right, this is a telltale sign of geometric random variables.

How many trials do he have to take until he gets a success? Let M be the number of shots it takes Jeremiah to successfully make his first three-point shot.

Okay, so they're defining the random variable here: the number of shots it takes, the number of trials it takes until we get a successful three-point shot. Assume that the results of each shot are independent. All right, the probability that he makes a given shot is not dependent on whether he made or missed the previous shots.

Find the probability that Jeremiah's first successful shot occurs on his third attempt. So, like always, pause this video and see if you could have a go at it.

All right, now let's work through this together. So we want to find the probability that, so M is the number of shots it takes until Jeremiah makes his first successful one. What they're really asking is to find the probability that M is equal to 3, that his first successful shot occurs on his third attempt.

So M is equal to 3. So that the number of shots it takes Jeremiah, not me, to make a successful first shot is 3. So how do we do this?

Well, what's just the probability of that happening? Well, that means he has to miss his first two shots and then make his third shot. So what's the probability of him missing his first shot? Well, if he has a 1/4 chance of making his shots, he has a 3/4 chance of missing his shots. So this will be 3/4.

So he misses the first shot, times he has to miss the second shot, and then he has to make his third shot. So there you have it, that's the probability: miss, miss, make.

So what is this going to be? This is equal to nine over sixty-fourths. So there you have it. If you wanted to have this as a decimal, we could get a calculator out real fast. So this is nine—whoops—nine divided by 64 is equal to zero, roughly 0.14.

Approximately 0.14, or another way to think about it is roughly a fourteen percent chance, or fourteen percent probability that it takes him, that his first successful shot occurs in his third attempt.

More Articles

View All
Weekend Wednesday
The way the work week works is the worst. Waking up on Monday, you’ve got five days in a row of work or school. It’s too much. For, by Wednesday, withered is your soul with two more days, nay three more days, until the weekend. But, alas. The weekend is a…
Touring a $44,000,000 Mansion in the Hollywood Hills
What’s of you guys? It’s Graham here. So I’m here with my colleague, Jason Oppenheim from Netflix’s hit show, Selling Sunset, and we’re on our way right now to see one of his forty million dollar listings up on the Sunset Strip here in Hollywood. It is, I…
Watch: Inside the World's Longest Sea Caves | Expedition Raw
Okay, let’s go for it. I actually went to New Zealand to study the other side of the island. But to satisfy my curiosity, I started exploring this coastline, and that turned out to be the day that I actually discovered the longest sea cave in the world. …
Atomic radii trends | Atomic models and periodicity | High school chemistry | Khan Academy
As we continue into our journey of chemistry, we’re going to gain more and more appreciation for the periodic table of elements. We’re going to realize that it gives us all sorts of insights about how different elements relate to each other. We’re going t…
Groups Search for Consensus, Individuals Search for Truth
Truth is very fought over. When we say truth, the biggest problem we’re going to run into is that what society wants for you is not what’s always good for you. Society is the largest group, and groups search for consensus; individuals search for truth. It…
The Man Who Hated The World (Animated Short Story)
The mind is its own place, and in itself can make a Heaven of Hell, a Hell of Heaven. John Milton. In a dirty prison cell, there lived a man who dedicated his whole life to isolating himself from the world. As opposed to most prisoners, he wasn’t put the…