This video is provided as supplementary material

for courses taught a Howard Community College and, in this video I’m going to talk about

the probability of the complement of an event. So I’ll start with this example. An airline reports that

94% of its flights arrive on time. What is the probability that will be late? So let’s call event of arriving on

time, “A”. So I can say that the probability of A, the probability of arriving on time, is 94%. I want to find the probability that a flight will be late. So let’s call that the probability of

not arriving on time, or the probability not A. The probability of not A. Now there are only two things that can

happen: a plane can arrive on time or it cannot arrive on time. Since those are the only two events

that I can have, if I add those two events together, I’m going to get 100%. So the probability of A plus the probability of not A is equal to 100%. If I take that equation and subtract the probability of A from both sides, I’ll find the probability of no A. So the probability of not A is equal to 100% minus the probability of A. Well, the probability of A is 94%.

So the probability of not A equals 100% minus 94%. If I subtract 94% from 100% I get 6%. So the probability of not A, the

probability of a plane arriving late, is 6%. Now when we talk about A and not A, we talk about these

as being complements of each other. In other words, if A is an event, its complement, the event not happening, is not A. We can write that as ‘not A’. If we want to use a different notation, I can just write anA with a bar over it. So an ‘A’ with a bar over it

means the complement of A. So I’ll change these other places where I’ve written ‘not’ and

just put a bar over the A. And so the general way you’re going to

find the complement of an event, the way you’re going to find what happens when

an event doesn’t occur, the probability of it, is going to be to subtract the probability

of the event occurring from 100%, if we’re doing

with a percent. If it’s not a percent,

just subtracted it from one. Okay, let’s do a couple more examples. In this example I’ve got a spinner and a circle. The circle is divided into five

sections. The sections are labeled A, B, C, D and E. And the probability of the spinner landing in section A when I spin it is 0.23. So I’ve got that

probability as a decimal, 23 hundredths. I want to find the probability of it not landing in section A. In other words, the probability of not A, or the complement of A, A with a bar over it. So all I have to do is realize that the probability of the A plus the probability of A not happening,

the probability of A-complement, or the complement of A, is 1. If I subtract the probability of A

from both sides, I’m going to have the probability of the complement of A equaling 1 minus the probability of A. The probability of A was 0.23. When I subtract 1 minus 0.23, I’m going to end up with 0.77. 0.77. So that’s the probability of the spinner not landing in section A, the probability of the complement of A. Let’s look at one more. In a bag containing 29 marbles, 5 of the marbles are red

and 2 are green. What is the probability of randomly

selecting a marble which is neither red nor green? Okay. So the first thing we have to do is find

the probability of getting a red marble and the probability of getting

a green marble. So the probability of red,

we’ll call that the probability of R, is is going to be 5 over 29, because there are 5 different ways

I can get a red marble and there are 29 total marbles I could select. The probability of getting a green

marble is going to be 2 over 29. There only 2 green marbles out of the 29 that I could choose. If I add these two probabilities

together, I’ll get the probability getting either a red or a green marble. And I’ll show that as the probability of the union of red and green. Add 5/29 plus 2/29, I just have to add 5 and 2. That 7 over 29. So the probability of getting either red

or green is 7/29. The complement of getting red or green would be the probability of getting

neither red nor green. I can write that as the probability of the complement of the union of red or green. And the way to find that is going to be

to subtract the probability of getting red or green from one. So instead of 1, I’ll use 29/29, to make the subtraction easy. I’ll subtract 7/29 from that. When I subtract 29 minus 7

I get 22. So the probability of getting neither red nor green, the probability of the complement of

red or green, is going to be 22 over 29. So the basic principle for all of the

examples I had was this: Take the probability of something happening,

the probability that you know, and just subtract that from one, if it’s a decimal or a fraction, or from 100% if you’re dealing

with a percent, and that will give you the probability of the event not

happening, the probability of the complement of the event.

And that’s all there is to it. Take care, I’ll see you next time.

Thank you so much.

thank you!

this was helpful. thank you!

thank u sir

thank you so much

Thanks😀👍🏾

Thanks ,it was very helpful

Thank you

i finally get it

thank you sir now I have an answer to my test tomorrow

Thank you very much 👏🏾👏🏾

Thanx sir for best video of probability

Thx for all the help! 🙂

Thanks

How did you get that it will be 100 percent is what I don’t understand