Probability (part 4) More on free throws.
Probability (part 4)
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- So we started doing some free-throw percentage
- problems in the last video, so let's continue.
- So the first time I said if I had an 80% free-throw
- percentage, what are my chances of getting three
- free throws in a row?
- And I said, well, it's 51.2% chance.
- Let's do another scenario, and let's just assume that my
- free-throw percentage stays at 80%.
- And let's say that-- I don't know-- let's say my team
- is two points behind.
- I'm making this up on the fly, so we're two points behind.
- No, let's say we're one point behind.
- And I'm up at the free-throw line, and I want to say, what
- is the chance-- and let's say I have three free throws.
- Someone fouled me when I was shooting a 3-pointer.
- So we're one point behind, there's one second left, and
- right when I was going to take the winning free throw-- or
- not the winning free throw.
- The winning 3-point shot, someone fouls me.
- So I get three free throws.
- And once again, I have an 80% free-throw percentage.
- My actual percentage is probably something
- more like 20%.
- But anyway, I have three free throws.
- So my question is, what are our chances of winning?
- What is the probability of my team winning?
- Not tying, winning.
- So in order to win-- well, actually let's
- do the tying first.
- So what's the probability of tying?
- How do you spell-- tying, OK.
- What's the probability of a tie?
- Well, the probability of a tie is going to be equal to the
- probability of me getting at least one free throw.
- You might say OK, that's the probably of getting exactly 1
- times the probability of getting 2 out of 3 plus
- the probability of getting 3 out of 3.
- But like we saw in-- I think it was either the last video or
- the video before-- that is identical equal to the
- probability or, let's see, 1 minus the probability of not
- getting any free throws.
- The probability of getting at least one is essentially the
- probability of me not missing all three.
- Hopefully that makes some sense.
- So let me erase all this stuff that I did up on top, and
- we can to figure out the answer to this problem.
- Let me erase all of this, erase all that.
- Erase that.
- Let me erase this.
- We know I have an 80% probability of making
- any one shot.
- So if we go back to the problem-- so this is my
- free throw percentage.
- So what is the probability of me not making any shots, not
- making any of my free throws?
- Well, my probability of not making one free throw is 20%.
- 20% chance of not making any free throws, or not making
- any-- say I take a shot, I have a 20% of no basket, or not
- making the free throw.
- So if I'm taking three shots, the shot of I miss all three
- is going to be equal to 20% times 20% times 20%.
- And that equals what?
- This 0.2 times 0.2 is 0.04 times 0.2.
- And then let's see.
- What's 0.04 times 0.2?
- Let's see, that'll be an 8 and I have 1, 2, 3 numbers
- by the decimal place.
- It's 1, 2, 3.
- So 0.008.
- So I have a 0.008 chance of missing all of the free throws.
- Or another way you could view this is, is this is equal to--
- a percentage is just this times 100 so there's 0.8% chance of
- missing all of the free throws.
- Or another way of viewing this is I have-- so what's my chance
- of making at least one?
- Well, it's going to be 1 minus this.
- So what's 1 minus 0.-- this is a 0.
- Well it's 99.2%.
- Yeah, that's 99.2%.
- Or you could also view it as 0.992.
- You take 1 minus this, you get 0.992, which is the
- same thing as 99.2% chance.
- So I have a 99.2% chance of at least tying the game.
- So it's pretty high if you have someone at the free-throw line
- with a 80% free-throw percentage and they
- have three shots.
- Now, what if I only had two shots?
- Let's say I got fouled when I was thinking a 2-pointer
- and I only have two shots.
- Well, in that case, in order to tie the game I have to get at
- least one, but I only have two shots.
- So it would be 1 minus the chances of me
- missing both shots.
- What's the chances of missing two shots?
- Well, the chance of missing two shots in a row-- it's 4%.
- 20% times 20%.
- It's a 4% chance of missing two shots, two in a row.
- So my probability of getting at least one, assuming that I am
- taking two shots, is going to be 1 minus this.
- I have a 96% probability of at least one shot if I take two.
- So that's also pretty high.
- And of course, what's my probability if I
- only have one shot?
- Well, it's 80%.
- So hopefully that gives you a little bit of framework next
- time you watch basketball game and you can pause your TiVo and
- figure out the probability when the person is making
- that last clutch shot.
- And it could be an interesting experiment for you.
- And actually, I was thinking, an interesting scientific
- experiment, or maybe a high-school science project,
- people have a free-throw percentage and that kind of
- implies that every time someone takes a free throw that those
- are mutually exclusive events, that they're independent of
- the previous time like we said with coins.
- But an interesting idea, you know in basketball people
- always say, he's hot now or he has a streak.
- And so there is this notion and I know I felt it, that there
- are times that you're probability increases or
- decreases, and it tends to be maybe dependent on whether you
- made or missed your previous shot.
- So one thing you might want to-- this is, I think, a
- legitimate science project-- is to either get the data from
- real NBA players and see if they really are mutually
- exclusive events.
- If the probability of making the next shot or the next free
- throw really is independent of whether they made or missed
- the previous one. or whether it actually is dependent.
- Or if you don't have all the data from the NBA or wherever,
- although I suspect you could find it, you could try it with
- yourself and your friends.
- Or maybe since you want to be unbiased, you'll do
- it with your friend.
- You'll see if the probability of them making the next free
- throw really is independent of whether they made the last one.
- Actually, I think that could be quite good and you can get
- quite involved in the analysis.
- So let me finish this up with another scenario.
- We talked about free throws, we talked about flipping a coin,
- and now I'll talk about dice because that is really another
- area where-- well, it's one interesting and you'll probably
- see some problems on probability.
- So, in general, when you're playing games involving dice
- it's always interesting to say, what's the probability if I
- have two six-sided dice, what's my probability of getting--
- I don't know-- a particular number.
- Let's say, what's the probability of getting a 7?
- So to think about that you have to say, well, what has to
- happen for the dice for me to get a 7?
- And I think here it might be interesting to
- draw a bit of a grid.
- So let's say that's my grid.
- Let me split it up into six.
- So let's see, that's splitting it up into one, into two.
- Each of these maybe split it up into three, so
- it would be like that.
- It won't be perfect, but close.
- Like that.
- Like that.
- And like that.
- And let me split it-- you'll see what I'm doing in a second.
- Actually, I didn't want to do that.
- That's good enough.
- Do this, this.
- I'm trying to make a 6-by-6.
- OK, and the reason why I'm doing this is because let's
- make this top axis, this horizontal-- each of the
- situations I can get on the first dice, although I'm going
- to roll them simultaneously, although it doesn't matter if I
- roll them simultaneously or one after the other, or I roll one
- dice one after the other.
- So this first dice I could get 1, a 2, a 3, a 4, a 5, or a 6.
- So this is dice one-- D1.
- And on the second dice, I could get a 1, a 2,
- a 3, a 4, a 5, or a 6.
- And this is dice two.
- And I'm running out of time, so I will see
- you in the next video.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
Have something that's not a question about this content?
This discussion area is not meant for answering homework questions.
Share a tip
When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
- disrespectful or offensive
- an advertisement
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site