what is the probability that an f2 seed chosen at random will be yellow This is a topic that many people are looking for. cfiva.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, cfiva.org would like to introduce to you 2 Examples of Probability With & Without Replacement. Following along are instructions in the video below:
This video. Im going to be taking a look at just a couple different different probability examples one with replacement and one without replacement and probably about the easiest to do this is to pretend that weve got a bag and its full of marbles alright. So in this first example.
I want to do a with replacement alright. Were going to be finding the probability of drawing. A red marble and then a blue marble and then a green marble in that order and with replacement.
Okay. Now what i mean is with replacement is whats my odds by reaching the bag. I pull out a marble okay and then with replacement means i put it back in before i draw the next marble okay.
So thats what were going to be doing in this first example so in my bag right here. Hopefully. The colors are going to show up pretty good here.
I have five blue marbles. I have four green marbles and i have six red marbles. Okay so that makes for a total of fifteen marbles in my bag.
So i have a total of fifteen all right so im going to start the very first thing i want to do is i want to know whats the probability that i reach in the bag. And i draw out a red marble on the first try. So there are 1 2.
3. 4. 5.
6. There are 6 red and there are 15 total in the bag ok now i reached in i pulled it out ok and then thats the probability that that first one was red now it says with replacement. So im going to take that marble and im going to put it back in the bag.
So i still have 15 marbles in there all right now times. Whats the probability of drawing a blue marble. When i come over.
I count how many blues 1 2. 3. 4.
So ive got 5 blue marbles and since it was with replacement. I put the first marble back in i still have 15 marbles so 15 on the bottom. Ok.
Now. I do a third time. Whats the probability of getting a green marble well there are four green marbles and there is still a total of 15 because it was with replacement so when i picked that marble out i put it back in the bag.
Which still leaves me a total of 15 in there. So thats for 15. All right this is straight multiplication youre going to multiply across stop your multiply across the bottom.
Youre going to get a 120 across the top its a graph calculator on that and across the bottom youll get three thousand three hundred and seventy five. So thats your probability. If you want to write it as a decimal you can convert it to a decimal which.
Means its about 0035 repeating and if you needed to write it as a percent and show that as a percent you could say about 35 repeating. Percent. Okay so thats the concept of with replacement okay now lets do the exact same thing.
But this time lets do without replacement okay. So. The question is well whats the probability of drawing.
A red marble and then a blue marble and then a green marble in that order without replacement. So im going to draw my first one and then im actually going to remove it out back okay so whats the probability of drawing a red marble okay so initially i had 15 marbles and theres one two three four five six. There are six red out of the 15 total all right now that first draw i drew it out it is out of my bag.
I am not putting it back in okay. Im not going to put it back in because its without replacement. So now im going to ask myself okay.
Whats the probability of drawing a blue marble well in the bag one two three four five. I have five blue ones all right. But because i did not put my first draw back in now.
I only have 14. Marbles. In the bag.
3. 4. 5.
6. 7. 8.
9. 10. 11.
12. 13. 14.
So the bottom number decreases by 1. All right now that second draw pull up the blue. One okay now do not replace it so its out of my bag.
Now whats the probability of drawing a green marble well in my bag. I have 1 2 3 4. I have 4 green ones all right.
But now because i did not replace that second one. I am down to 13 barbels one two three four five six seven eight nine ten eleven twelve thirteen so now im down to 13 so the without replacement changes. What you have in your bag okay again straight multiplication multiply across the top.
Were going to get 120 multiplying 15 times 14 times 13. Were going to get 2730 all right so thats probability. If you want to need to convert it to a decimal thats going to be about point o.
4 3. 9. And if we want that probability as a percent thatd be roughly four point four percent okay so just two real quick examples.
There of calculating some probabilities with replacement verses without replacement definitely thanks for watching hope this was helpful in clearing up. The with and without replacement and be sure. And give me a thumbs up and share with your friends thanks.
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