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
JEFF VS. ADAM: Nerd Wars!
It’s a nerd force! Oh good, what style are we doing it now? Alright, so welcome to Nerds War. There’s a very special Nerds War. We didn’t prep because I sliced my finger—[ __ ] oh um, so we’re doing a Nerds War extreme! Adam vs. Jeff! Said, I’m playing A…
Acceleration | Physics | Khan Academy
I decided to raise my regular household car with a sports car, say Ferrari. Well, clearly, it’s no match for me. It has a very high top speed, but what if we both agree, for the sake of this race, to limit our top speed to say 80 miles an hour? Now, do yo…
Multiplying 10s | Math | 4th grade | Khan Academy
Let’s multiply 40 times 70. So, 40 times we have the number 70. So, we could actually list that out, the number 70, 40 different times and add it up, but that’s clearly a lot of computation to do, and there’s got to be a faster way. So, another way is …
Divers Find a Wreck 90 Meters Down | Drain the Oceans
It is a very deep dive with a lot of repercussions that come up too fast. Bubbles would form inside your blood, inside your tissues, and cause ill effects. To get to 90 meters, you’d be looking at 4 or 5 minutes to get down there. It’s very dark because y…
Representing points in 3d | Multivariable calculus | Khan Academy
So, a lot of the ways that we represent multivariable functions assume that you’re fluent with understanding how to represent points in three dimensions and also how to represent vectors in three dimensions. So, I thought I’d make a little video here to …
Using the reaction quotient | Equilibrium | AP Chemistry | Khan Academy
The reaction quotient is symbolized by the capital letter Q, and it tells us whether a reaction is at equilibrium or not. If the reaction is not at equilibrium, it also allows us to predict which direction the net reaction will go to reach equilibrium. F…